People have been advised to also refrain from holding religious fire rituals or burning dry crops.
The advisory was issued on Monday on orders from the state chief minister.
It came after reports that 67 people had died in the state in fire-related incidents in the past month.
Several parts of India, including Bihar, are in the grip of a severe heat wave with temperatures crossing 40C.
"After a review of fire incidents, we've seen that most of them were caused by cooking fires. That's why we have issued an advisory to villagers that they must finish cooking before 9am and put out the fires when they finish," senior disaster management official Vyas, who uses only one name, told BBC Hindi's Manish Shandilya.
The review found that some fires also started during Hindu religious rituals or while burning dry crops, he added.
In one particularly tragic incident, 13 people were killed in a fire which started during a religious ceremony in Aurangabad district.
Officials said if a fire broke out because of someone flouting the advisory, then those found guilty would be penalised under disaster management rules.
But correspondents say it is unclear how authorities will penalise a poor villager who has lost everything in a fire.
The disaster management authorities in the northern Indian state of Bihar have advised villagers to avoid cooking between 9am and 6pm to prevent outbreak of fires during the scorching summer.