Batt, who made his much-awaited return from a long-term injury last month, will remain at the Broadfield Stadium for the next four weeks as he continues to regain his match fitness.
Crawley boss Steve Evans said: "He has good technique and explosive pace. That gives defenders in the Championship a headache and will cause League Two defenders even more problems.
"In fairness to the lad he had a number of options in respect of clubs wanting to sign him so I am delighted he has joined us.
"I am grateful to Millwall manager Kenny Jackett who spoke very favourably to Shaun about coming to Crawley.
"I watched Shaun last week when he was outstanding in a closed-doors match. I made my move then but with him being cup-tied it did not have to happen until yesterday and we are delighted he is here."