Yandel Rohena died Wednesday morning at St. Luke's Baptist Hospital in San Antonio, the San Antonio Express-News reported.
He and his brothers, two sets of identical twins, were delivered at the hospital Jan. 15.
"It's the worst thing in my life yesterday," the boy's father, Khristian Rohena, told the newspaper Thursday. "You just think of all the things you could have done different to keep him longer."
Quadruplets are extremely rare, although they have become more common because of the use of reproductive technology. Rohena said the quadruplets were conceived without fertility drugs.
Babies in multiple births are also far more likely to be premature and to have low birth weights, greatly increasing the risk. Rohena said last week he and Shontae Minor were advised in September when an ultrasound revealed she was carrying quadruplets to have two of the fetuses aborted.
The couple decided against the procedure when they learned it would not be covered by Medicaid because Minor and the fetuses were all healthy and because a Houston specialist told them all the quadruplets appeared to have a good chance of surviving the pregnancy.