Police say Mejia-Ramos is considered a suspect in the stabbings. He was arrested by U.S. Marshals and local police on a New York warrant. Charges are pending.
Fayette County, Texas, authorities say the suspect, who goes by at least one other name, was located after he turned on his cellphone.
It wasn't immediately known if he had a lawyer.
The bodies of 1-year-old Yaslin Mejia and 2-year-old Daniela Mejia and their mother, 21-year-old Deisy Garcia, were discovered Sunday night in their Queens apartment.