The shooting occurred Sunday morning at Starrville Methodist Church in Starrville, about 100 miles east of Dallas.
“Our hearts are with the victims and the families of those killed or injured in this terrible tragedy,” Abbott said.
The governor said police “apprehended the suspect,” but he did not release more details about the identity of the alleged shooter.
“The State of Texas is working closely with first responders and local officials to ensure that justice is served and that the Starrville community has the resources it needs during this time,” Abbott said.
Authorities have not specified how many people were hurt or the severity of the injuries.