The city rivals kick off their league fixture at 12:30pm and the match is expected to attract a full crowd.
Chief Inspector Murray Starkey, match commander for the game, said: “Flares, fireworks or any controlled containers, which could cause harm if thrown, are strictly forbidden from the ground.
“Anyone attempting to carry those items into Tynecastle stadium, or who is in possession of alcohol or attempting to enter whilst drunk, is liable to arrest and prosecution.”
Scottish football is currently under the microscope due to a raft of antisocial behaviour incidents at games.
Recent incidents include a Buckfast bottle being thrown at Celtic player Scott Sinclair during a game against Hibs at Easter Road, while a number of ripped-up seats were thrown by supporters during an Aberdeen v Rangers match at Pittodrie.
And interim Celtic manager Neil Lennon was Hibs boss when he was struck by a coin thrown from the crowd during the Edinburgh derby last Halloween.
Police have said there will be a “high visibility presence” in and around Tynecastle on Saturday and officers will be assisting stewards to conduct searches on those entering the stadium.
Officers are reminding fans they will be enforcing the capital’s drinking by-laws and so antisocial street drinking will not be allowed.
Chief Insp Starkey added: “There’s always a fantastic buzz in Edinburgh in the run-up to the derby, with tens of thousands heading to the match and many more watching from home.
“Ensuring the safety of all those who will attend the match is our priority, and it’s essential that supporters act in a responsible manner that does not put themselves or others at risk.
“I want to ask fans from both sides of the city to act in a responsible manner and enjoy the match.
“Please allow some extra journey time to allow for any road congestion. Turnstiles open at 11.30am, and I would hope that spectators will choose to arrive early at the stadium.
“This is one of the most exciting fixtures of the Scottish football calendar and we want both sets of fans to enjoy the game safely and in the proper spirit.”
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