AK Antony said federal detectives would probe Gen VK Singh’s allegation, which he made to The Hindu newspaper.
Gen Singh said the bribe was offered to make him clear the purchase of 600 “sub-standard” vehicles.
There has been an uproar in the parliament over Gen Singh’s remarks.
Mr Antony said the army chief’s allegations were “serious” and ordered a probe into the matter by the Central Bureau of Investigation (CBI), the Press Trust Of India reported.
Earlier, the parliament was adjourned with opposition parties demanding an explanation from the government.
Gen Singh told the The Hindu that the lobbyist offered the bribe in return for approving the purchase of 600 “sub-standard” vehicles of a “particular make”.
He said the army already had 7,000 of the vehicles in question and many had been sold at “exorbitant prices with no questions asked”.
“Just imagine, one of these men had the gumption to walk up to me and tell me that if I cleared the tranche, he would give me 140m rupees [$2.7m; £1.7m]. He was offering a bribe to me, to the army chief,” he said.
“He told me that people had taken money before me and they will take money after me.”
Gen Singh said he had immediately reported the matter to the defence minister, Mr Antony.
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