Between 5pm and 9.15pm on Wednesday, three men were cycling on the path near Murrayburn and Wester Hailes when they were confronted by a group of youths.
On each occasion, the cyclists were pushed into the canal and sustained minor injuries.
Police are now appealing for witnesses following the attacks.
Sergeant Alex Dickson, from the South West Community Policing Team, said: “The youths may have thought this was a bit of fun, but it could have resulted in serious injury, or worse, and we are treating these incidents very seriously.
“In response, we are going to deploy high-visibility patrols in the area to engage with cyclists and members of the public and deter any further incidents.
“If you witnessed anything suspicious on the Union Canal cycle path on Wednesday evening, or if you believe you can provide us with a description of the suspects, then please contact police immediately.
“In addition, we are also eager to hear from anyone else with any other information relevant to this investigation.”
Those with information should contact Wester Hailes Police Station via 101 and quote incident numbers 3223, 3469 or 4077 of the 27th March.
Alternatively, an anonymous report can be made to the charity Crimestoppers on 0800 555 111.
Green councillor and Edinburgh canal champion, councillor Gavin Corbett, also condemned the attacks. He said: “As someone who cycles on the canal towpath every day I’m alarmed and disappointed to hear of these incidents. I’m glad there was no serious injury but only by luck.
“The canal towpath has generally become so much safer over the last 20 years partly because so many people use it. However, it’s a prompt to look further at towpath improvements such as visibility and lighting, so that it continues to be a popular route for walking, cycling and running.”
Sign up to our newsletter: enter your email in the box at the top of this article to get daily updates straight to your inbox.