Hasina expressed “deep condolence” at the death of Sushma and extended sympathy to her family in a message early on Wednesday.
Bangladesh signed many important deals with India during the tenure of Sushma, a star minister in Modi’s 2014-2019 cabinet.
These included the historic Land Boundary Agreement which enabled the two countries to swap 162 enclaves.
The former Indian minister died at a New Delhi hospital on Tuesday night after auffering a heart attack.
"She (Sushma) was a good friend of Bangladesh. With her death Bangladesh has lost a good friend," Hasina said in the message.
“Bangladesh will recall her contributions in taking the relationship between the two countries to a new height,” her Press Secretary Ihsanul Karim quoted the prime minister as saying.