Boko Haram fighters burnt down almost the entire town on Wednesday, after over-running a military base on Saturday, Musa Alhaji Bukar said.
Bodies lay strewn on Baga’s streets, amid fears that some 2,000 people had been killed in the raids, he added.
Boko Haram launched a military campaign in 2009 to create an Islamic state.
It has taken control of many towns and villages in north-eastern Nigeria in the last year.
The conflict has displaced at least 1.5 million people, while more than 2,000 were killed last year.
On Monday, lawmaker Maina Maaji Lawan said Boko Haram controlled 70% of Borno state, which is worst-affected by the insurgency.
Mr Bukar, a senior government official in the area, said that fleeing residents told him that the town, which had a population of about 10,000, was now “virtually non-existent”.
“It has been burnt down,” he said.
Those who fled reported that they had been unable to bury the dead, and corpses littered the town’s streets, he said.
Boko Haram was effectively in control of Baga and 16 neighbouring towns, Mr Bukar said.
Government troops abandoned the military base in Baga on Saturday, when the militants launched an assault.
It hosts the Multi-National Joint Task Force (MNJTF), made up of troops from Nigeria, Chad and Niger, although the BBC understands there were only Nigerian soldiers there at the time of the attack.
Set up in 1998 to fight trans-border crime in the Lake Chad region, the force more recently took on Boko Haram.
Thousands have fled Baga – many to Maiduguri, the capital of Borno state, and others to Chad.
A large number reportedly drown as they crossed Lake Chad following Saturday’s raid.
Nigeria’s President Goodluck Jonathan declared a state of emergency in Borno and two neighbouring states in 2013, vowing to defeat the militants.
However, Boko Haram has stepped up attacks since then, and there are fears that many people in the area will not be able to vote in next month’s general elections because of the conflict.