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."

Baker, 23, and Thornton, 20, trained with Wales ahead of the 2015 World Cup, but were omitted from the squad.
Both have signed three-year deals, taking the total of players on NDCs to 16, with Ospreys contributing half.
Their salaries funded 60% by the Welsh Rugby Union and 40% by the regions.
Baker has been capped three times and Thornton led Wales Under-20 in the 2015 Six Nations.
The duo's deals were announced a day after Ospreys hooker Scott Baldwin and back-five player James King signed dual contracts.
Baldwin, 27, was his country's first-choice hooker at the recent World Cup and has signed until 2019.
Lock or back-rower King, 25, has secured a deal until 2018.
The deals, which give the Welsh Rugby Union more control over players, were introduced to help stem the exodus of stars such as Toulon's Leigh Halfpenny from Wales.
Newport Gwent Dragons number eight Taulupe Faletau turned down a dual contract in May 2015 and Bath's recent bid to sign him was vetoed by Wales coach Warren Gatland.
Baker, Thornton, Baldwin and King have signed against a backdrop in which fly-half Rhys Priestland has taken an 18-month Test rugby sabbatical to concentrate on playing for Bath after leaving Scarlets.
Gatland said: "Dan and Rory are players of significant potential.
"We look forward to continuing to work with them at national squad headquarters, but also to watching them continue to flourish for the Ospreys."
Fly-half Biggar is expected to sign a contract extension, but lock Jones is considering his future beyond the end of the 2015-16 season.
Wales captain Sam Warburton was the first of the nation's current generation to commit to a dual deal.
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.
[NEXT_CONCEPT]
Ospreys number eight Dan Baker and uncapped lock Rory Thornton have become the latest Welsh players to sign national dual contracts (NDC).