Matthew Tryson Bryant apparently died in his sleep, Gruden said. The coach did not have further details. Matthew was born June 16.
"We're shocked and very saddened by this," Gruden said. "It's just a horrible tragedy, and I can't explain it."
Bryant issued a statement later on Wednesday.
"Melissa and I are overcome with the amount of support we have received from the community during this difficult time," it read. "We would like to thank our Buccaneers family and the [owner] Glazers for their support and outpouring of love.
"Tryson enriched our lives for the short time that he was with us and
we will never forget his smile. We know Tryson's death has deeply
touched the community and we appreciate the love and prayers from our
Gruden said he was not sure if Bryant will play in Sunday's game against Green Bay. The player's situation would be addressed later in the week, the coach said.
"The entire Buccaneer family is deeply saddened by this tragedy," Buccaneers general manager Bruce Allen said in a statement. "The Bryants have been an inspiration to our entire community through their commitment to their family and their exhaustive efforts working with children and those in need in the Bay area. Our thoughts and prayers are with Matt and Melissa during this difficult time.''
Bryant, a seventh-year pro in his fourth season with Tampa Bay, kicked a winning field goal in overtime against Chicago last Sunday. Two years ago, he made the third-longest field goal in NFL history, a 62-yarder to beat Philadelphia.
Pat Yasinskas covers the NFC South for ESPN.com. Information from The Associated Press was used in this report.