Ynetnews, in a report attributed to an unidentified Egyptian newspaper, said Shaqaqi, 20, was arrested at his home in the al-Yarmouk refugee camp in Damascus.
A relative said security forces had detained his son without allowing family members to see him or providing information on his whereabouts or those of other Jihad operatives imprisoned in Syria.
It wasn't reported when the younger Shaqaqi was taken into custody.
Though the Syrian government and the militant group have close ties, Syrian authorities denied the group's request to release militants when the uprising against President Bashar Assad began in March.
The violent Syrian crackdown on protesters has continued despite the arrival of Arab League monitors. Al-Arabiya reported up to 43 people died in Friday's violence, including five members of Syria's security forces.
The elder Shaqaqi was shot dead in Malta Oct. 26, 1995.