The campaign has garnered nearly five million signatures and has seen opposition leader Suu Kyi -- who is constitutionally barred from becoming president -- challenge the military to support altering the charter, which was drawn up under the previous regime.
"Because it's related to the workings of parliament, which listens to the voice of the people, MPs can consider the people's voice," said Shwe Mann, the speaker of parliament's combined houses and leader of the army-backed ruling party.
Shwe Mann was a senior figure in the former junta who shed his uniform to become part of Myanmar's quasi-civilian government that took power in 2011, ending decades of outright military rule.
He did not specify how parliament, dominated by army officials and ruling party members, would scrutinise the petition.
Shwe Mann added that the petition would not affect the deliberations of a parliamentary committee set up to recommend changes to the controversial constitution.
The committee, which is believed to be against changing the provision that bars Suu Kyi from becoming president, will make recommendations to parliament, which will then debate the proposals.
- 'Benchmark' polls -
Suu Kyi is trying to change key sections of Myanmar's constitution ahead of 2015 elections that are widely expected to be won by her National League for Democracy (NLD) -- if they are free and fair.
The Nobel laureate has urged soldiers to support the petition.
"I would like you all to consider whether getting more opportunities than ordinary citizens is really fair," she told a rally in Rangoon in May, earning a rebuke from the country's election commission.
The NLD believes revising that clause will open the way for further changes to other constitutional provisions, including the ring-fenced proportion of soldiers in parliament and the effective bar on Suu Kyi leading the country.
As it stands, she is ineligible because of a clause in the 2008 charter blocking anyone whose spouse or children are overseas citizens from leading the country. Suu Kyi's two sons are British.
To alter the constitution a majority of more than 75 percent of parliament is required.
Unelected soldiers make up a quarter of the legislature and therefore have the last say on any changes.
The speaker made his comments at a press conference following a weekend meeting with US Secretary of State John Kerry on the sidelines of Association of Southeast Asian Nations (Asean) talks in Naypyidaw.
Kerry said he praised officials and the country's President Thein Sein on sweeping reforms that have seen the removal of most Western sanctions.
But he raised a number of concerns -- including ethnic and religious unrest, the arrests of journalists and dissidents and the constitutional amendment.
Next year's elections would be a "benchmark" for the world to measure Myanmar's progress, Kerry said.
The president will be elected by parliament after the polls.