The International Campaign for Human Rights in Iran says Mr Mirsayafi, 29, died on Wednesday.
His lawyer Mohammad Ali Dadkhah said officials at the Evin prison told him Mr Mirsayafi had committed suicide and he demanded and immediate inquiry.
There was no immediate comment from Iranian authorities.
In quotes published by AFP, Mr Dadkhah said another Evin prisoner with medical training "had warned officials in the jail of the state the young blogger was in".
The ICHRI says he suffered from severe depression.
Mr Mirsayafi was sentenced last month to 30 months in prison after being convicted of insulting supreme leader Ayatollah Ali Khamenei and other clerics.