South Wales Police warned drivers to allow extra time for their journeys on Monday (31 October) evening after reports of flooding between junction 45 and junction 43.
It added that disruption was likely across other parts of the M4 as a result.
More rain is forecast for Tuesday, largely in the south, with those in north Wales most likely to escape the heavy showers.
The Met Office is also warning to expect strong winds along the western coast of the country and parts of north and south Wales on Wednesday.
This means delays on the roads and rail, short-term power cuts and large waves along the coast are all likely.
Storm Claudio’s move eastwards on Tuesday is expected to leave in its wake a showery day for much of the UK, with Wales and areas in southern and central England predicted to see the most frequent rainfall.
There are three active flood alerts in Wales for areas surrounding the Gwendraeths, Loughor, Amman, Bran and Gwydderig rivers.
Conditions are unlikely to improve by midweek as low pressure moving in from the west is forecast to bring wet and windy weather.
The Met Office has issued a yellow weather warning for wind for parts of Wales, lasting from 7am to 6pm on Wednesday.
Cyclists, motorbikes and caravans have been advised that they may be stopped from using the Britannia Bridge all day Wednesday starting at 9am, as well as Thursday morning.
There is also likely to be heavy rainfall for some on Wednesday afternoon.
Met Office Deputy chief meteorologist Steven Keates said: “Within the warning area, gusts are expected of between 55 and 65mph.
“This is associated with low pressure moving towards the north west of the UK, which is bringing with it some heavy rain on Wednesday, especially across parts of south west Scotland, Cumbria and western Wales, although much of the UK will see some rain through the day."
The windy weather comes after the UK enjoyed above-average temperatures as October came to an end, with the mercury reaching the low 20s in places like Cardiff.