The man was described as light skinned, thin build and about 180cm tall.
"This robbery is now the third that has occurred in the last few days where Countdown supermarkets have been targeted," Mr Thompson said.
Countdown is reviewing security at their stores and is increasing security as a result of these recent robberies.
Detective Shane Brown of Feilding police said on Sunday a person attempted to rob a Palmerston North Countdown with an "edged weapon" like a knife, but ran from the scene after being confronted by a security guard.
"And then they went straight to the next one in Palmerston North and they had the same weapon with them, and they were successful with that (robbery), he said.
Police want to speak with anyone who was in the Feilding Countdown last night and who may have seen the robber run from the scene.