Elected president Morsi was ousted and imprisoned by the Egyptian military during a military coup carried out in mid-2013.
"We call on free people worldwide and international rights organizations, including the UN, to investigate the rights violations to which President Morsi is being subjected," the family said in a statement.
The family issued the statement on Sunday, one day after Morsi’s youngest son, Abdullah, said the authorities had denied his request -- for the second time in two weeks -- to visit his imprisoned father.
Family members say they have been prevented from visiting Morsi in prison since late 2013.
"Since then, the authorities have turned down all our requests to visit the president," the statement read.
There has been no comment by the Egyptian authorities on the family’s assertions.