The exact number of those injured was yet to be ascertained, a senior official said. Earlier it was reported that over 60 people suffered injuries in the mishap.
State Chief Minister Shivraj Singh Chouhan has ordered a judicial probe into the accident.
A large number of devotees had gathered at the temple on the occasion of 'Somwati Amavasya' when the mishap occurred during the circumambulation of the Kamtanath Pahad (mountain).
"Ten people were killed in the stampede," District Collector M L Meena said.
Devotees, mostly women, encircle the mountain by lying and rolling on the path for worship. The presence of a large crowd resulted in the stampede in the area leaving 10 people dead, he said.
Chouhan has announced an ex-gratia of Rs 2 lakh each to the kin of those killed in the stampede; Rs 50,000 to the seriously injured and Rs 10,000 to those who suffered minor injuries.
The exact number of people injured in the stampede will be known later, as Collector and other senior officials have rushed to the spot from Satna to take stock of the situation, a state government official said.