The taxi driver has undergone surgery for a broken jaw, a spokesman for taxi firm Dantaxa said.
Danish newspaper Ekstra Bladet cited unnamed sources saying Bendtner was arrested early on Sunday, charged with violence, but later released by the police.
Bendtner currently plays for Norwegian side Rosenborg but was not picked for the Denmark team that went on to beat Wales 2-0 in Aarhus.
A spokesman for Copenhagen police said there had been a number of reported cases during the night involving violence against taxi drivers, but he declined to comment on individual cases.
A spokesman for Rosenborg declined to comment and the Danish Football Association DBU also declined to comment. Bendtner could not be reached for comment.
Thirty-year-old Bendtner, who was left out of the Denmark side that reached the knock-out stages of the 2018 FIFA World Cup in Russia, burst onto the scene in 2005 as a precocious talent at Arsenal, but was soon on loan to Birmingham City.
He went on to represent Sunderland, Juventus, Wolfsburg and Nottingham Forest but his goals were often overshadowed by tabloid tales of drink-fuelled escapades.
After signing for Rosenborg, Bendtner has started to rediscover his best form, winning the Norwegian title in 2017 and netting three goals in 11 games last season.
