Up to 40mm (1.5in) could fall, with a yellow be aware warning in place until 22:00 BST.
Forecasters are uncertain about how heavy and persistent the rain will be.
The warning covers Carmarthenshire, Pembrokeshire, Powys, Caerphilly, Merthyr Tydfil, Neath Port Talbot, Rhondda Cynon Taff, Bridgend, Cardiff, Swansea and Vale of Glamorgan.
A moist southerly airstream is set to bring the bulk of the rain in a four-hour period, with the Met Office saying it will issue further updates to the warning throughout Monday.
It said it could lead to standing water and spray on roads, making travel conditions tricky.
Outbreaks of heavy rain will hit parts of south, mid and west Wales through Monday, the Met Office has warned.