The links from the M5 junction 15 south to the M4 junction 20 west, and the M5 junction 16 north to M4 junction 20 west are also closed.
National Highways said the M4 is shut in both directions between junctions 20 and 22, while the M48 is closed both ways between junction 1 and the M4.
Parts of the M4 and M48 motorways near Bristol are likely to remain closed until the early hours of Sunday morning, Avon and Somerset Police said.
The road closures are likely to cause significant delays in and out of Wales tonight, with closures starting on the English side of the Prince of Wales Bridge and the Severn Bridge.
Several drivers reported a body on the carriageway between junctions 20 and 21 of the M4 - between Almondsbury and Awkley - at about 6.40pm this evening.
