The explosion, at South Fork Dairy near the town of Dimmitt, also left one person in critical condition.
Authorities believe that machinery in the facility may have ignited methane gas.
Nearly three million farm animals died in fires across the US between 2018 and 2021.
Castro County Sheriff’s Office said they had received a report of a fire at the farm at about 19:21 on Monday (00:21 GMT Tuesday).
Photos posted by the Sheriff’s Office show a huge plume of black smoke rising from the ground.
When police and emergency personnel arrived at the scene, they found one person trapped who had to be rescued and flown to hospital in critical condition.
While the exact figure of cows that were killed by fire and smoke remains unknown, the Sheriff’s Office told the BBC that an “estimated 18,000 head of cattle” had been lost.
Speaking to local news outlet KFDA, Sheriff Sal Rivera said that most of the cattle had been lost after the blaze spread to an area in which cows were held before being taken to a milking area and then into a holding pen.
“There’s some that survived,” he was quoted as saying. “There’s some that are probably injured to the point where they’ll have to be destroyed.”
Mr Rivera told KFDA that investigators believed the fire might have started with a machine referred to as a “honey badger”, which he described as “vacuum that sucks the manure and water out”.
“Possibly [it] got overheated and probably the methane and things like that ignited and spread out and exploded,” he said.
In a statement sent to the BBC, the Washington DC-based Animal Welfare Institute said that – if confirmed – a death toll of 18,000 cows would be “by far” the deadliest barn fire involving cattle since it began keeping statistics in 2013.
“We hope the industry will remain focused on this issue and strongly encourage farms to adopt common sense fire safety measures,” said Allie Granger, policy associate for AWI’s farm animal program. “It is hard to imagine anything worse than being burned alive.”
According to the AWI, nearly 6.5m farm animals have been killed in barn fires since 2013, of which about 6m were chickens and about 7,300 were cows.
Between 2018 and 2021, nearly 3 million farm animals died in fire, with 1.76m chickens dying in the six largest fires over that time period.
