Under Niyazov's arrangement, which many Turkmen people were said to have found confusing, January was called Turkmenbashi (which Saparmurat called himself).
April was renamed Gurbansoltan after his mother, September was called Rukhnama after his spiritual guidance book and Monday was just called "the main day".
"Thousands of citizens have written to ask to return to the Western month names and call the days of the week the way our ancestors did," Akja Nurverdyeva, the parliament speaker, said on television.
During his 21-year rule, Niyazov built up a personality cult around himself which included the building of a large number of statues of him across the central Asian nation.
He also declared himself Turkmenbashi - or "Head of the Turkmen" - and banned opera, ballet and circuses.
Berdymukhamedov has tried to reduce the state-sponsored adulation of his predecessor, reversing some of Niyazov's more eccentric policies.
Last year he abolished the state-funded dance and music concerts held to honour Niyazov and repealed a law requiring students and state employees to recite the country's oath of loyalty to the president.