The measure against humanitarian affairs and poverty alleviation minister Betta Edu came days after another senior official was suspended over corruption charges.
Tinubu came to power last year promising to crack down on graft in Nigeria.
The opposition Peoples Democratic Party, PDP, had called for Edu to be sacked and prosecuted "over the alleged looting of almost $50 million" from a social investment fund "meant for the wellbeing of the poor."
The opposition party claimed this included approximately $661,000 "audaciously diverted by her (Edu) to a private account."
Tinubu has ordered a probe after documents allegedly related to the transfer of funds were published in local media. AFP could not independently verify those claims.
Last week Tinubu suspended the head of the social investment fund agency Halima Shehu over alleged corruption. She was arrested and released on bail, according to local media.
The PDP accused Tinubu of presiding over "unprecedented treasury looting."
But Tinubu's spokesman said the president had suspended Edu in line with his "commitment to uphold the highest standards of integrity, transparency, and accountability."
Tinubu ordered Nigeria’s anti-corruption body to investigate the ministry and vowed to make changes to "win back lost public confidence" in schemes for poor households, spokesman Ajuri Ngelale said.
Tinubu came to power last year promising reforms and swiftly suspended several officials, including former central bank chief Godwin Emefiele and ex-head of the Economic and Financial Crimes Commission,EFCC, Abdulrasheed Bawa.
But Edu is the first minister the president has suspended.
Nigeria remains one of the lowest ranked on Transparency International's widely watched corruption perceptions index.
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