Defence ministry officials termed the meeting as a "courtesy call".
They said the meeting was sought by Lt Gen Bakshi, contrary to initial claims by army sources that Parrikar had sought the meeting.
Lt Gen Bakshi also met with Army Chief Gen Dalbir Singh Suhag after meeting Parrikar.
Dalbir Singh is set to visit the Eastern Command in Kolkata shortly as part of his farewell tour. The army chief will hang his boots on December 31.
A section of military experts feel that Lt Gen Bakshi may seek premature retirement. However, the process may take a month or two, sources said, adding that during this period he may go on leave.
Lt Gen Bakshi was initially the front runner for the post of the army chief. However, keeping aside the trend of seniority being the lone criteria, the government appointed Vice Chief of Army Lt Gen Bipin Rawat, a batch junior to Lt Gen Bakshi, as the new chief.
Lt Gen Rawat, an infantry soldier, was found best suited among three officers to deal with challenges like cross-border terrorism in Jammu and Kashmir and the situation with Pakistan, both areas which the government felt will be under focus for the next 2-3 years.
Another section of military experts claimed that Lt Bakshi may become the new Chief of Defence Staff, a post that has been hanging fire for the last many years.
While the creation of such a post is in "active consideration" of the government, it is unlikely that it will happen soon, they claimed.
The Centre had on December 17 appointed Lt Gen Rawat as the new army chief superseding his two senior officers -- Lt Gen Bakshi and Southern Command Chief Lt Gen P M Hariz.
Photograph: http://indianarmy.gov.in
Will General Bakshi be India's first CDS?
Why I support General Rawat's appointment
Some advice and a word of caution for the next Army Chief
Will Gen Rawat be a better chief than Gens Bakshi and Hariz?
Why the government chose General Rawat