The Turkish fans tried to force their way to the United team amidst the chaotic scenes, as Sir Alex Ferguson and his players had to leave the building through a separate terminal.
Police used tear gas to stop the crowd from becoming dangerous and causing any damage, with Galatasaray's football director Abdurrahim Albayrak asking the fans to behave sensibly.
"In every aspects, we are a top class club," he said. "We had to welcome our opponents warmly, not in that way.
"After my reminder, our supporters understood the importance of welcome and calmed down.
"[Manchester United] hosted us with respect and our first aim is to repay their hospitality."
Ferguson added that this time was not as "frightening" as it was in 1993 when United were greeted with 'Welcome to Hell' banners.
"Yes, absolutely," he said. "We dodged it, we came underground!
"We didn't get the meeting from the fans this time, but in 1993 it was incredible and quite frightening.
"We have been here a few times now, though, and are now used to the Turkish atmosphere. It is fanatical, but it is no issue for us."
United have already progressed to the last 16 as Group H winners with four wins out of four.