Jay Cutler’s feeling the heat from his DUI arrest — he is still allowed to drive, but there are strings attached, TMZ has learned.

Law enforcement sources tell TMZ the former NFL star can’t get behind the wheel without using an interlock ignition device. So, if he doesn’t pass the Breathalyzer in the car, that car’s not moving!

As we told you, the police report we got revealed Kristin Cavallari‘s ex-husband rear-ended another car Thursday night in Franklin, Tennessee — and when officers showed up, they caught a strong whiff of booze. Police also said he had bloodshot eyes and was slurring his words.

TMZ broke the news … Jay ended up spending some time in jail after he was busted for DUI and 3 other offenses.

The other charges are failure to exercise due care, violation of implied consent law (for declining to take a blood or breath test), and possession of a handgun while under the influence.