Azerbaijani President Ilham Aliyev told a meeting of his Security Council: "We will not tolerate this unprovoked act of terror and aggression against Azerbaijan. Our armed forces have been instructed to prepare and implement appropriate retaliatory measures."
"We are ready to demonstrate our strength against any hostile force - and they should not forget this in Iran," he said.
Iranian Deputy Foreign Minister Kazem Gharibabadi denied his country had targeted Nakhchivan.
"We do not attack our neighbouring countries," he told Azerbaijani outlet AnewZ.
Azerbaijani authorities said they were investigating the types of drones used in the attack.
They said one drone fell on the terminal building of Nakhchivan International Airport, which is approximately 10km across the border from Iran, and another drone landed close to a school building in a nearby village.
One was downed by the Azerbaijani army and another hit civilian infrastructure.
The country is a major oil and gas producer, mostly exporting energy to Turkey and Europe via the Baku-Tbilisi-Ceyhan pipeline.
Any damage to its infrastructure could drive global energy prices even higher.
Azerbaijan's Foreign Ministry earlier demanded that Iran "clarify the matter in the shortest possible time, provide an explanation and take the necessary urgent measures to prevent such incidents from recurring in the future", adding that the incident "contributes to increased tensions in the region".
It handed a note of protest to the Iranian ambassador to Azerbaijan.
The four injured were taken to hospital, where they are in stable condition, the Health Ministry in the landlocked exclave of Azerbaijan bordering Armenia, Iran and Turkey told Reuters.
Video footage verified by Reuters showed black smoke rising near the airport and damage to the skylight inside the terminal building.
The exclave of Nakhchivan is separated from mainland Azerbaijan and borders Armenia, Turkey and Iran.
The United States and Israel have been carrying out air strikes against Iran since Saturday.
In response, Iran has fired missiles and drones at several countries in the region.
with Reuters
