The former French international reacted badly to comments about his dress sense by presenter Jake Humphrey ahead of the Newcastle-Liverpool fixture.
In a statement, the newly-created sports channel said: "BT Sport would like to apologise for any offence that was caused during this morning's broadcast.
"David Ginola apologised straight afterwards as he realised this was an inappropriate action."
Ginola, 46, who had a reputation for suave skills during his seven years in the Premiership, gesticulated after Humphrey jokingly remarked that he "clearly wasn't expecting to be seen full length".
The Frenchman played for Newcastle, Tottenham Hotspur, Aston Villa and Everton before retiring in 2002.
BT Sport said it had received complaints from viewers but would not comment on how many.
Ginola later tweeted: "Heading home from a cracking live game @btsport @mrjakehumphrey. So terribly sorry for my rude unacceptable gesture, didn't know i was live.
I very humbly ask everyone @btsport @mrjakehumphrey & all the fans to accept my wholehearted apologies for the rude, unacceptable gesture."