The error was made by RingGo payment system, which is managed by City of Edinburgh Council's contractor NSL.
Motorists who tried to use RingGo on Tuesday will have their tickets cancelled.
The council said it clearly stated on its website and parking machines that 27 December was a paid parking day.
The council said about 300 motorists had been affected by the blunder.
A council spokeswoman said: "Details relating to parking restrictions during the festive period are advertised very clearly through our website and social media and are provided on ticket machines throughout the city.
"We are aware, however, that there was an error for a time with the RingGo payment service managed by our contracted partner NSL.
"We are liaising with NSL to ensure that RingGo users who were issued with a parking ticket, due to the system failure on Tuesday, have their tickets cancelled."
An NSL spokesman said: "NSL has confirmed that parking restrictions and charges in the city of Edinburgh do apply on Tuesday 27 December and Monday 2 January as stated on all Pay and Display machines and on the City Of Edinburgh Council's website.
"Full enforcement procedures apply on both dates in order to maintain safe and fair access for anyone visiting the shops and facilities in and around the city centre.
"The company has confirmed that it has been made aware of an incorrect instruction on the RingGo app and RingGo website and has asked for the instructions to be amended as a matter of urgency."
Hundreds of drivers have been issued parking tickets after an app wrongly told them they could park for free in Edinburgh on the day after Boxing Day.