Parrikar, the first Indian defence minister to Bangladesh in the last 45 years, was greeted by Bangladesh Defence Forces' Principal Staff Officer Lt Gen Md Mahfuzur Rahman and other government officials.
The defence minister is leading an 11-member high-powered delegation.
According to an army press release here, Parrikar will meet President Abdul Hamid and Prime Minister Sheikh Hasina during his stay in the country.
He is also scheduled to meet with the prime minister's defence and security advisor Maj Gen Tarique Ahmed Siddique (retd) for bilateral talks.
The Indian military officials will also meet with the heads of Bangladesh's Army, Navy and Air Forces to discuss ways to improve military cooperation.
Top Defence Ministry officials in New Delhi had said the focus of the trip was to deepen security ties and firm up a defence cooperation agreement that is likely to be signed when Prime Minister Hasina visits India next month.