Terry Levinthal, director of the Cockburn Association, the town’s heritage watchdog, said there had already been a heightened problem.
Cleaning workers in Edinburgh went on an 11-day strike last week after they turned down a pay offer from Cosla, the council’s umbrella organisation.
City workers have been offered an improved 5 percent pay rise and unions are considering the possibility.
Meanwhile, rubbish spills out of overflowing bins and piles up in the streets, with city center areas particularly hard hit given Edinburgh’s festivals.
Mr Levinthal said the amount of litter in the Old Town and other festival hotspots had increased “exponentially”.
He told the BBC’s Good Morning Scotland program that Edinburgh already had problems with litter and litter collection.
When asked if he feared the situation could become “a huge public health problem”, he replied: “Yes it is – already the vermin problem has increased.”
He said the seagulls came out “in force”, adding: “Even before the strike there were problems.
“Our members and stakeholders have complained, particularly in the old town, where we have seen a number of structures erected for hotel businesses – these provide fantastic places for the city’s population of mice and rats to hang out in. hide and eat all the offerings that were left for them, if I can put it that way.
“And we will see, as a result of that, that in a few weeks there will be a massive expansion of the vermin population because there is so much food on offer.”
Mr Levinthal said everyone had a role to play in trying to manage the situation.
He urged residents not to throw waste such as cardboard and polystyrene on the streets, to leave extra capacity for waste that cannot be stored in properties.
He added: “But we also need to communicate to the tourism and events sector that there is a strike.
“And if those businesses that have commercial collection facilities can actually maybe step up, because it’s also in their interests to showcase the city in the best possible way, that can really help.
“Even when the strike ends, it will take a long time for everything to be collected and recovered, so the more we can do now, the better in the short term.”