The left-hander made 15 starts for Los Angeles this season, and was a member of the Angels' rotation since 2014.
The Angels' scheduled game against the Texas Rangers on Monday was postponed following the news of Skaggs' passing.
"I am deeply saddened by today's tragedy in Texas," MLB Commissioner Rob Manfred wrote in a statement.
"All of us at Major League Baseball extend our deepest condolences to Tyler's wife Carli, their family, their friends and all of his Angels' teammates and colleagues."