Andrew Irving, who played as a second-half substitute in the 2-1 victory at Balmoral Stadium, was not properly registered.
Hearts chief executive Ann Budge said it was an “administrative error” which causes the club “much embarrassment”. She issued an apology on behalf of the club.
The matter will be discussed by the Scottish Professional Football League on Monday where sanctions will likely be imposed on Hearts.
In 2016 Stranraer and Cove Rangers were each fined £2000 for listing ineligible players in the Betfred Cup.
Stranraer’s Nathan Brown was an unused substitute in their win over Annan Athletic while Cove Rangers’ Lewis Dunbar was also an unused sub in a defeat by Alloa.
Budge said in a statement: “It is with much embarrassment that we have to advise that during last night’s Betfred Cup group stage match away to Cove Rangers, Hearts inadvertently fielded an ineligible player.
“Due to an administrative error on the club’s part at the end of the January transfer window, Andrew Irving entered the field of play in the 65th minute as an unregistered player.
“Andrew was given an extension contract in January, 2018 and his extension paperwork was all properly completed and in order. However, it was not loaded onto the online SFA registration system at the time. His official registration, therefore, ran out on 9th June, 2018. Unfortunately, this was not picked up in advance of last night’s game.
“While stringent processes are already in place to try to prevent something of this nature occurring, clearly mistakes can happen. An additional step in our internal procedures will be implemented immediately to try to ensure this cannot happen again.
“The club would like to apologise to its supporters, to Cove Rangers Football Club and to the footballing authorities for this inadvertent breach of the rules.
“A hearing with an SPFL panel has been scheduled for Monday, July 23rd and will be attended by representatives of the club, where sanctions against Hearts will be determined. Until then, no further comment will be made.”