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.

The London derby will kick off at 17:15 BST on Saturday, 22 April.
Spurs are one of only four clubs to beat Premier League leaders Chelsea this season - a 2-0 victory in January.
The second Wembley semi-final between Arsenal and Manchester City, which will kick off at 15:00 BST on Sunday, 23 April, will be shown on BT Sport, with highlights later on BBC One.
Tottenham won the 1967 FA Cup with a 2-1 win over Chelsea, while the Blues beat Spurs 5-1 in a semi-final at the new stadium on their way to winning the competition in 2012.
It is the third meeting between the sides the season - Chelsea won 2-1 at Stamford Bridge in November - and Spurs will hope to have striker Harry Kane back from an ankle injury.
Football Focus will come live from Wembley on the Saturday as part of the build-up to the semi-final.
Chelsea beat holders Manchester United 1-0 on Monday to reach the semi-finals, a day after Tottenham thrashed League One side Millwall 6-0 in their quarter-final.
Outbreaks of heavy rain will hit parts of south, mid and west Wales through Monday, the Met Office has warned.
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The FA Cup semi-final between Chelsea and Tottenham at Wembley Stadium will be broadcast live on BBC One.