The movie tells the story of an outrageous gay Austrian fashion correspondent hoping to make it big in Hollywood, and one scene featured the character joking about stars who adopt foreign children.
The actor collects an African baby out of a box on an airport baggage carousel before turning to the camera and saying, "Angelina's got one, Madonna's got one, now Bruno's got one."
Madonna welcomed Malawian tot David Banda into her family in 2006 but recently had her application to adopt three-year-old Mercy James turned down by a court in the country.
And Cohen is now said to have reached out to the star to apologise for his jokes about the sensitive situation, according to British newspaper the Daily Mirror.
A source tells the publication, "Sacha is always out to make great comedy - and if he upsets people along the way, so be it. But when word reached him that Madonna thought his sketch was insensitive, he sent her a bouquet of flowers to say, 'No hard feelings'."
Cohen and Madonna are said to have been pals since the singer invited him to star in the video for her 2000 hit Music.