They claim authorities at Alexandria's Al-Hadra prison recently ordered soldiers to storm jail cells and beat prisoners with sticks and batons.
"A number of the prisoners were seriously injured in the head and face," the families said in the statement.
The wife of one prisoner said she had seen traces of torture on her husband's body when she visited him Sunday, the Turkish news agency Anadolu Agency reported.
"Prisoners were being beaten because they refused to be interrogated, as they do not recognize the prosecution's legitimacy," she said.
An unidentified prison official described the torture claims as rumors, and accused Morsi's Muslim Brotherhood of attempting to turn public opinion against the government.