Progress M-44 was launched by a Soyuz-U carrier rocket from Site 1/5 at the Baikonur Cosmodrome. Launch occurred at 08:09:35 GMT on 26 February 2001. The spacecraft docked with the Aft port of the Zvezda module at 09:49:47 GMT on 28 February. It remained docked for one and a half months before undocking at 08:48 GMT on 16 April. It was deorbited at 13:23 GMT the same day. The spacecraft burned up in the atmosphere over the Pacific Ocean, with any remaining debris landing in the ocean at around 14:11 GMT.
Progress M-44 carried supplies to the International Space Station, including food, water and oxygen for the crew and equipment for conducting scientific research. It was the first Progress-M spacecraft to visit the ISS, previous resupply missions having used the Progress-M1.
Payloads are separated by bullets ( · ), launches by pipes ( | ). Manned flights are indicated in bold text. Uncatalogued launch failures are listed in italics. Payloads deployed from other spacecraft are denoted in brackets.