The Republic of Ireland Under-21 international has not featured for the Lions in the league but has been on the scoresheet for his country.
O'Brien, 19, netted twice against Holland last week to cap a memorable debut and he linked up with the Reds for training on Wednesday.
"The reports from our scouts and (director of football) 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," manager 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 added: "I'm delighted to be here and I'm hoping that I can get some games for Crawley over the next few weeks and show the fans here what I am made of.
"In terms of my career this is a fantastic opportunity for me and one I'm determined to grab with both hands."