Senior General Maung Aye, second-in-command of Myanmar's military government, and Mohammad Hamid Ansari, India's vice president, signed the accord.
India also called for Myanmar to push forward with plans for national reconciliation, saying the country's rulers should engage Aung San Suu Kyi, Myanmar's detained pro-democracy leader, the statement said.
During his visit, Maung met Manmohan Singh, India's prime minister, who reiterated New Delhi's commitment to support Myanmar in telecommunication and IT sectors, the Indian statement said.
An Indian defence ministry official separately told the AFP news agency that Maung "reviewed bilateral military co-operation" in his talks with the Deepak Kapoor, the Indian army chief.
"The talks included Indian military exports to the government in Yangon," the official said.
Over the past decade, India has increased its economic and military ties with Myanmar.
New Delhi has been eager to secure the co-operation of the Myanmar military to help contain separatist groups fighting New Delhi's rule in northeastern India near the Myanmar border.
The infrastructure agreement was signed the same day as Aung San Suu Kyi's political party urged voters to reject a military-backed draft constitution, saying it was undemocratic and written under the government's direct control.
The charter will be voted on in a referendum next month.
The military government has also announced general elections in 2010.
Myanmar arrested 3,000 people in a crackdown on protests led by Buddhist monks last year.
India repeated on Thursday its criticism of US and European sanctions that were tightened after the security sweep.
"The vice-president conveyed that India did not believe that sanctions were helpful and that it may well prove to be counter-productive," the Indian foreign ministry statement said.