It is the fifth migrant boat to sink in two days, with seven people confirmed dead so far, and 67 still missing.
Authorities believe the boat was heading for Italy.
The Tunisian coast guard has reportedly stopped 56 boats from leaving the country, bound for Italy, in the past two days.
Houssem Jebabli from the Tunisian National Guard said that more than 3,000 migrants had been detained attempting to leave the country.
Tunisia has become a launch pad for migrants to leave, bound for Europe. United Nations data shows that at least 12,000 migrants who arrived in Italy this year left from Tunisia, compared to 1,300 in the same time period last year.
Last month, Tunisian President Kais Saied accused sub-Saharan African migrants living in the country of causing a crime wave and described them as a demographic threat.
His comments were widely criticised by the African Union and denounced as "racist hate speech" by human rights groups.
Speaking at a summit in Brussels on Friday, Italy's far-right Prime Minister Giorgia Meloni warned there may be a "migratory wave" towards Europe if Tunisia's political and economical situation does not stabilise.Tunisia is currently facing its worst financial crisis after negotiations for a loan with the International Monetary Fund (IMF) stalled.
The US Secretary of State Antony Blinken has also warned that Tunisia urgently needs to reach a bailout deal with the IMF.
Tunisia has also faced significant political challenges since July 2021 when Mr Saied seized most powers, shut down parliament and moved to rule by decree.