There was an "apparent deterioration" in his health following his failure to attend the last two cabinet meetings, the group said.
Mr Buhari took about seven weeks of medical leave in January, and flew to the UK for treatment.
When he returned home in March, he said he had never been so ill in his life.
Mr Buhari has not disclosed his illness, but hinted that he had had a blood transfusion.
The president had not been seen in public for the last week, and his absence from the cabinet meetings, as well as the weekly Friday Muslim prayers, "has fuelled further speculation and rumours" about his medical condition, the group of 13 Nigerians said in a statement.
The group included some of the Nigeria's most influential civil society figures, including lawyer Femi Falana, political analyst Jibrin Ibrahim, and Transparency International Nigeria head Anwal Musa Rafsanjani.
The 13 said they felt "compelled" to ask Mr Buhari "to heed the advice of his personal physicians by taking a rest to attend to his health without any further delay".
Mr Buhari's aides have not yet commented on the statement.
Last week presidential spokesman Garba Shehu said Mr Buhari was "taking things slowly, as he fully recovers from the long period of treatment" in the UK.