Four deaths occurred in the town of Moknine in the Monastir governorate, while a fifth death was reported in Nabeul town, civil defence spokesman Khalil Mechri told AFP.
The National Institute of Meteorology has told AFP that some Tunisian regions had not seen so much rain since 1950.
Tunisia's civil defence said some of the hardest hit regions were Monastir, Nabeul and greater Tunis.
Heavy rain began Monday night and continued until Tuesday night, with showers on Wednesday, leaving schools and businesses shut and transportation disrupted.
The four missing people are fishermen, local media reported, after a fifth was rescued in Teboulba, south of Monastir.
The civil defence told AFP that emergency services have rescued some 350 people trapped by floodwaters since the flooding started.
Mechri said while the bad weather was now less intense, "the level of alert remains high".
AFP footage and videos widely circulated on social media showed significant flooding to homes and roads, with cars stranded in water.
President Kais Saied visited several affected areas on Tuesday, including Moknine and Teboulba, local media said.
The rainfall has been record-breaking, but Tunisian streets often flood after heavy downpours, largely because of the state of the country's infrastructure.
Drainage and stormwater networks are often old and poorly maintained, particularly in rapidly expanding urban areas, with waste sometimes clogging the system.
Rapid urbanisation of some areas has also led to less rainwater being absorbed into the ground, increasing runoff.
The dramatic deluge comes as Tunisia grapples with a seven-year drought, worsened by climate change and marked by a sharp decline in water reserves at dams nationwide.
In neighbouring Algeria, several regions have also been hit by massive downpours and floods, with authorities reporting two deaths as of Wednesday in the country's western Relizane and Chlef areas.
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