The officer was injured in the Meadows on Saturday after police were called to deal with mass gatherings and sporadic fights that were breaking out.
A video, shared widely on social media, was taken by Scottish rapper on his Instagram @jaad_rapper, and shows the dramatic scenes that include police breaking up the fights by wrestling people to the ground.
At one point, a man is smashed over the head with a glass bottle by someone he had been fighting with.
David Hamilton, Chair of the Scottish Police Federation said: "Police Officers didn't write these health regulations but for the last year we have been asked to enforce them for the protection of all.
“Public hostilities towards the restrictions were foreseeable and have been growing for some time.
"They have increasingly culminated with some in our society taking out their anger and frustrations on Police officers.
“Yesterday in Edinburgh, one of our members was hospitalised with a facial injury, and countless other unvaccinated officers were put at risk, for simply doing their jobs to keep others safe.
“It is simply not good enough that politicians have offloaded these predictable problems onto police officers, especially when they have failed in their responsibility to protect and support those of whom they have asked so much.”
Chief Inspector Sarah Taylor of Edinburgh Police Division said: “We are aware of the extent of the disorder seen in the Meadows this weekend and we absolutely condemn this.
“Officers were called to a number of incidents over the course of the day and responded quickly and professionally in the face of some blatant anti-social behaviour.
“Hundreds of people were moved on or dispersed from the area.
“Three people have so far been charged in connection with anti-social behaviour and a serious assault, and we are working to trace others involved in various incidents.
“In particular, we’re eager for anyone who saw a 22-year-old man being attacked around 7.30pm in the Middle Meadow Walk area and also a 17-year-old man being seriously injured in the park around 6.40 pm, to come forward.
“Anyone who witnessed these incidents, who has seen information online or has footage which may be relevant is asked to contact Police Scotland on 101, quoting incident 1635 of 3 April, 2021.
"Information can also be passed anonymously to the independent charity Crimestoppers on 0800 555 111.
"Be assured that there will be a continued police presence at The Meadows over Easter and the coming weekends, as a minimum.
"We've been working with the council and are committed to tackling these issues together, both in the immediate future and long-term. There will be zero tolerance.”
The MP for Edinburgh South, Ian Murray, said police and the council should come up with an action plan to deal with trouble on the Meadows and the mess left behind from large gatherings.
He tweeted: “It’s a huge thank you to all the volunteers & council staff who cleaned up the Meadows again last night.
“We need an action plan from the council, police, govt, retailers to resolve the mess, violence, residential streets being used as a toilet & significant impact on local area.”
The litter and destruction left on the Meadows was cleared up by concerned residents surrounding the area.
Local Murray MacDonald, who runs Autism on Water and headed out to clear the Meadows more than once last week, made the effort once again to clear the litter from the beauty spot.
He took to the Facebook page The Meadows Share to plea with people to take their rubbish home with them, though conceded he would head out in the evening with a bag to collect what he could.
Pictures taken on Sunday morning show council workers also spread across the area gathering the last of it to make the area safe and clear again.
Council leader Adam McVey condemned the scenes in the Meadows yesterday and praised the efforts of local residents and council teams in clearing up the mess left behind.
He said: “In the run up to the Bank Holiday Easter weekend we urged people to be responsible, follow the national guidance and respect and care for our parks.
"So it was shocking to see what happened in the Meadows last night with people behaving appallingly- fighting amongst themselves and with the police.
"This behaviour was simply disgraceful.
"I want to thank the local residents for the great community spirit they showed by picking up litter and our street cleansing teams who were out early this morning clearing everything up.
"I also want to thank the park rangers and police for their work keeping the majority of responsible residents safe.
"We’ll continue to work closely with Police Scotland to keep our parks safe for all to enjoy and remind everyone to be responsible over the rest of the holiday weekend and through spring and into summer.”
Diane Gray, who lives in the area, said the Meadows has been very busy on sunny days with "hordes of young people congregating".
"I don't blame them for wanting to meet up, just wish they would be more responsible," she said.
Ms Gray said there had been problems with litter, including human waste, broken glass and "drug paraphernalia".
"Personally I am older/restricted mobility and I keep well away on days when it's busy because it doesn't feel safe," she added.
Many in the community reacted strongly to the scenes, and the video that was posted across Facebook, Twitter and Instagram.
One person commented: “Disgusting. Used to be a place you could take your kids and grandchildren. Not now.”
Someone else added: “There needs to be a vast increase in police patrols in the meadows from around 5pm.”
Another comment read: “Too much drugs and alcohol mixed together is lethal shame for the police dealing with this!”
Scottish Government coronavirus guidelines loosened on Friday, as the Stay at Home message changed to Stay Local.
The rules allow four people from two households to meet outdoors, as long as they remain two meters apart.
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