District Magistrate of Amroha BK Tripathi told media persons that the cows fell ill in the evening after eating fodder.
Officials of the Animal Husbandry Department and veterinarians were rushed to the scene to treat the cattle, news agency PTI reported.
Superintendent of Police Aditya Langeh later confirmed to PTI that more than 50 cows at the shelter died.
According to the DM, the management at the cow shelter has procured fodder from a person identified as Tahir. "An FIR has been lodged against Tahir and efforts are being made to arrest him," the DM said.
"The village development officer, who is in charge of the cow shelter, has been suspended," he added.
"Chief Minister Adityanath has directed the animal husbandry minister to reach the spot after taking cognisance of death of cows in Amroha," the CM's Office tweeted on its official handle.
The office said the chief minister has ordered to send a team of veterinarians for the treatment of ailing cows.
"The CM has said that anyone found guilty for the incident will not be spared," read another tweet.