The 19-year-old has not played for Millwall's first team this season, but impressed for his country last week when he scored twice against Holland for the Republic Under-21s.
"The reports from our scouts and Steve Coppell for a while now on Aiden were very positive and their manager Kenny Jackett believes he now needs to go out and play league football," Crawley boss Richie Barker told the club's official website.
"He is very highly regarded at Millwall and he will get opportunities here between now and the end of the season. We have 17 games to play in 10 weeks which is going to stretch the squad so Aiden will get his chance.
"He is a hard working striker who is a very good finisher and I'm sure when he gets his opportunity he will do well for us and we look forward to working with him."
O'Brien began training with his new club on Wednesday.