She made the appeal in an interview with NHK, a Japanese public broadcaster, in Tokyo on Thursday during her four-day official visit to Japan.
Many minority Rohingya Muslims have crossed the border to Bangladesh to escape the military crackdown against Rohingya militants that Myanmar started in 2017.
Hasina said the cost of operating refugee camps for more than one million Rohingya is rising as energy and food prices have soared on the back of the Ukrainian situation.
The prime minister said her government has already started discussions with the Myanmar military about returning the refugees. She said Myanmar has agreed to take them back, but nothing has materialized so far.
During the visit, the Bangladesh prime minister met her Japanese counterpart Kishida Fumio on Wednesday and both the leaders agreed to elevate bilateral relations to a strategic partnership.
Hasina said she wants to conclude an economic partnership agreement with Japan by 2026. She said Bangladesh has a large population of young people, and there are huge markets in South and Southeast Asia.