Font linked a quote from Pique which said Barca must "look to the future because the past only serves to learn from our mistakes" with his own campaign for the presidency, which carries the slogan "Si al Futur" (Yes to the future).
"Victor, with all respect, these words have nothing to do with what you are trying to transmit with this tweet," Pique wrote on Twitter on Friday. "I ask you to delete it and not to use my image for your benefit."
Font quickly replied with an apology and removed the tweet from his personal account and from the "Si al Futur" account.
"Gerard, we used this reflection because it is in line with our thoughts," he said. "In no case did we want to create any problem for you. We have deleted it."
Font is one of three candidates to replace Josep Maria Bartomeu, who resigned as president in October, when club members vote on March 7, with Joan Laporta and Toni Freixa the other two.
Laporta, who was previously Barca president between 2003 and 2010, is leading the polls, ahead of Font, and Pique's social media intervention could serve as a further boost to his campaign given the centre-back's popularity among the club's supporters.
On the pitch, Barca will look to continue their good start to 2021 on Sunday when they travel to Real Betis in search of their sixth straight win in La Liga.
Four of those five wins have come away from Camp Nou and, after next Wednesday's Copa del Rey semifinal at Sevilla, Barca will have played 11 of their 12 games in the calendar year away from home or at a neutral venue.
Most of those games have involved late kick-offs and early morning returns to Barca, with Koeman's side yet to have a free midweek since the turn of the year.
"At some point, UEFA or the Spanish league will have to do something because they are killing the players with this schedule," Koeman said in a news conference on Saturday.
Barca will be without the injured quartet of Pique, Sergi Roberto, Philippe Coutinho and Ansu Fati when against Betis. A win will move them within seven points of leaders Atletico Madrid, although they will have played two more games.