The centre-back felt a problem with what appeared to be his hamstring and could not continue.
Varane could not continue and Ole Gunnar Solskjaer was forced into making a change and had to alter his formation to go with it.
Mason Greenwood came on in his place and it had an almost immediate effect.
Atalanta had gone 1-0 ahead through Josip Ilicic, when Varane was still on the pitch.
It was a David De Gea error that saw the Italian side take the lead as his shot from the edge of the box somehow squirmed underneath him.
The France World Cup winner came off in the 38th minute and just a few minutes after he was replaced United were back on level terms.
United levelled in first-half stoppage time as an outstanding team move ended with Greenwood superbly playing in Bruno Fernandes, whose brilliant backheel teed-up Cristiano Ronaldo to fire home.
Duvan Zapata thought he had given Atalanta the win before Ronaldo popped up again to rescue a 2-2 draw for United.
Losing the centre-back, who was a summer signing from Real Madrid, will be a huge blow for Solskjaer who has seen both him and Harry Maguire struggle with injuries at points this season.