"Will the government carry out the ruling, or will it as usual procrastinate? That's the question that everyone's waiting to have answered," said Maqsoud.
Legally, the ruling is binding and effective immediately, but the Egyptian government has in the past ignored court orders involving political opponents.
Detained by the government
On trial are 39 Muslim Brotherhood members.
Thirty four, including Khairat el-Shatir, the Brotherhood's third-in-command, have been detained by the government since last November, while five others are to be tried in absentia.
Mubarak referred the 39 members of the Muslim Brotherhood, which is banned in Egypt, to a military court on terrorism and money-laundering charges in February, the first such referrals since 2001.
The detainees appeared before a closed military tribunal in April, but the session was postponed after only a single defence lawyer turned up.
Constitutional changes
The Egyptian government stepped up its campaign against the Brotherhood, targeting Brotherhood finances and arresting hundreds of the group's members, after the Brotherhood won around twenty per cent of the seats in parliament in the 2005 elections.
A set of constitutional amendments approved in a referendum in March gave Mubarak greater powers, including the power to transfer anyone suspected of "terrorism" to military courts.
But his order transferring the detainees to a military courts was made before those changes were made to the constitution.
The overruling of the president by the courts is a rare occurrence in Egypt, but Tuesday's ruling has pleased the relatives of those on trial, many of whom had been concerned that a military tribunal would not have been impartial.