According to Channels TV, he resigned on Sunday night on the grounds of ill-health.
It is also reported that arrangements are ongoing to swear in the next most senior justice of the Supreme Court, Justice Olukayode Ariwoola, as the acting Chief Justice of Nigeria.
Chief Justice Tanko Muhammad has resigned after being rocked by corruption and misconduct charges from other at least 14 other Supreme Court justices.
A spokesman for the Supreme Court confirmed this on Monday morning, but said additional details would be made public as to its cause.
There are many publish series of articles last week from a protest authored by Supreme Court justices against Mr Tanko, accusing him of corruption, misconduct and neglect of personnel welfare.
The rare charges were seen by court analysts as historically explosive, warning that it could worsen its reputation.
Mr Tanko replied to the justices, accusing them of dancing naked in the marketplace and absolving himself of any wrongdoing.