It has also received five reports of customers receiving electrical shocks.
Users should unplug the cords and contact Microsoft for a free replacement, the US Consumer Product Safety Commission added.
Microsoft announced the recall at the end of January, but did not reveal how many of complaints it had received.
The recall is of power cords sold with the Surface Pro, Surface Pro 2 and Surface Pro 3 tablets before March 2015 in the US and Canada and July 2015 outside of those countries.
Microsoft is recalling more than two million power cords sold with Surface tablets worldwide after 56 reports of them overheating and emitting flames.