"The plane has crashed, 23 people on board are dead," the duty officer at a local police branch, who identified himself as Kadykov, told Reuters by telephone.
"The cause of the crash is unknown," he said.
Azerbaijan, situated on the Caspian Sea, is a former Soviet republic with a thriving oil and gas industry. It is not known if any foreigners are among the dead.
A reporter with independent Azeri television channel, Lider, told Reuters by telephone from the scene of the crash that he saw medical teams removing bodies from the wreckage of the plane near the seashore at Nardaran, on the outskirts of Baku.
"Witnesses of the crash told us that before the plane crashed they saw it making slow circles as if the crew were trying to direct it away from residential areas," Mekham Mekhtiyev said.
The aircraft was heading to Aktau in Kazakhstan across the Caspian Sea with 18 passengers and five crew members on board.
A police spokesman said that wreckage was found along the Caspian coast, but there was no evidence of survivors.
Russia's Ria news agency said the plane fell off radar screens 20 minutes after take off.
It is reported to have come down near the village of Kyurdakhany, about 15 kilometres from Baku, Ria said.
The Associated Press news agency described the plane as an An-140 twin engine turbo prop.
The An-140 is a relatively new short range passenger plane designed in the 1990s. The aircraft, which has two propeller engines and can carry up to 52 passengers, is produced jointly by Ukraine and Russia.