The South African Weather Service (SAWS) said Desmond had brought 277mm of rain to the city of Beira - the fourth largest city in the country.
The World Meteorological Organization (WMO) said the storm will last about 48 hours.
Brit In Beira, a British mother who blogs from Mozambique, posted in a message on Facebook on Tuesday: "Tropical storm Desmond has brought some epic rain ....
"We are fine, our house has a few leaks but all safe and sound. My heart just breaks for the people's houses that have been completely flooded or washed away. As always in these events it's always the most vulnerable and desperate that suffer the most in the hands of mother nature."
Please remember to pray for Mozambique.. pic.twitter.com/rx03WqiFPc
โ Dudley_tha_Zimbo (@dudleychi) January 22, 2019
Accuweather meteorologist Jason Nicholls said at around midday on Tuesday that Desmond was weakening over Mozambique.
"Low strengthening over Mozambique Channel and likely becomes a depression and storm before swinging just south of Madagascar on Thursday."
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