He also said, "May God be with the people of Sutherland Springs".
A spokeswoman for Connally Memorial Medical Center in nearby Floresville told Fox News that "we have accepted a number of patients from the shooting".
Local media report that law enforcement has closed off the the scene, where emergency vehicles line the streets and witnesses have told of several helicopters overhead.
The church is located in the 500 block of 4th Street in the small, south Texas town about 40 miles east of San Antonio.
Sunday's attack comes just a month after the one of the deadliest mass shootings in USA history, when 58-year-old Stephen Paddock killed 59 people and at least 527 others. The first news reports of the shooting were between noon and 12:30 p.m.
U.S. President Donald Trump, now in Japan, tweeted to say that the FBI was investigating the shooting.
In a statement posted on Twitter, Texas Gov. Greg Abbott said: "Our prayers are with all who were harmed by this evil act".
Abbot is en route to Sutherland Springs to speak with law enforcement and the victims.
A witness at the scene reported a 2-year-old was also shot.
A sheriff's department dispatcher says everyone is at the scene and unavailable to comment.
The Wilson County Texas Sheriff's Office declined to provide Reuters with further details on the shooting.