The measure however would need to be approved by Egypt's ruling military and in a signal of the military council's likely response, a minister in the army-appointed cabinet called the new law "a deviation" that targetted one or two people.
The legislation approved on Thursday, an amendment to the law governing political rights, would also block the candidacy of anyone who served as a prime minister in the decade prior to Mubarak's removal from power. That would rule out Ahmed Shafiq, who is also running.
However, it did not cover former ministers, meaning it would not affect leading liberal contender Amr Moussa, Mubarak's foreign minister for a decade until 2001.
The presidential election gets under way on May 23 with two days of voting expected to be followed in June with a run-off between the top two candidates.
The field is broadly made up of Islamists, officials who served under Mubarak and independent leftists and liberals.
The legislation approved on Thursday was a direct response to the last-minute decision by Suleiman to seek the presidency, a step which both Islamists and secular-minded reformists alike see as a threat to their hopes for democratic reform.
The Muslim Brotherhood, which controls nearly half the seats in parliament, was outlawed under Mubarak.
As head of the Egyptian intelligence, Suleiman was one of Mubarak's closest aides. The former president appointed him as his deputy after the eruption of the popular uprising that led to his downfall on 11 February 2011.
Suleiman's critics have said he will only be able to win the vote through the kind of rigging that happened during elections in the Mubarak era. However, his candidacy appears to have a struck a chord among voters concerned at the rise of Islamist influence and who see him as the best bet for stability.
Khairat al-Shater, the Muslim Brotherhood's presidential candidate, has said Suleiman's candidacy is an insult to Egyptians who rose up against Mubarak. The Brotherhood has called a protest on Friday in response.
Suleiman has said he will win support among Egyptians who he believes are angered at attempts by the Muslim Brotherhood to dominate the post-Mubarak era.
The military council has been governing with Mubarak's presidential powers since it took control of the country. That means parliament has only limited authority, though the chamber was elected in Egypt's most democratic election in six decades.