The accused, identified as Raj Kumar, was caught red handed on Tuesday by volunteers of the shelter here that is run by Kartaliya Baba Ashram.
The volunteers had been keeping a vigil on the shelter after they came across CCTV footage that showed the man raping several cows.
The accused was caught when he returned to the shelter and attempted to rape cows again.
Raj Kumar was reportedly beaten up by those who caught him before handing him over to the police.
Ayodhya SSP Jogendra Kumar said that the man has been arrested and booked under sections 376 and 511 of the Indian Penal Code for cruelty against animals.
"The CCTV footage shows the man doing dastardly acts with seven cows, one by one. We have caught him and brought to the police station. The act has left us distraught, we are unable to understand this," the Kartaliya Baba Ashram's priest Ramdas told reporters.
The accused, who hails from Gonda district, told the police that he was under the influence of alcohol.
"I was drunk, I do not know what I did. I only remember that I was beaten by both, people who caught me and the police," Raj Kumar told the media.
( With inputs from IANS )