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"It is with our deepest sorrow that we send our baby girl Violet Eva Carazo to play with the angels," the statement said. "We were able to spend two weeks with our sweet baby girl and for that we are forever thankful. Please respect our privacy during this difficult time. Your thoughts and prayers are very much appreciated."
No cause of death was revealed, however, in an Instagram post from March 13, Carazo revealed that Violet was born seven weeks early.
"Happy One Week Old Birthday to our Baby Girl Violet," the post's caption read. "Thank U for making me a Dad and bringing me an entire new perspective during your first week of Life. We love you so much!"
Carazo added several hashtags to his post, including "#7WeeksEarly" and "NICUBaby."
The couple announced the baby's birth on March 10 on Instagram, McGinty sharing a photo of herself, Carazo and Violet.
"Our sweet Violet Eva has arrived," the caption said. "Your thoughts and prayers are appreciated."
Reps for A + E Networks, parent company to the "Little Women" franchise, did not immediately respond to Fox News' request for comment.