Dozens of shots were reportedly heard in the wooded area behind the cemetery, next to Brennan Estates, a residential area.
Delaware State Police said it received the initial call about 10:15 a.m. Friday and that one or more people had been shot.
Police radio reported one patient was rushed from the cemetery by ambulance, USA Today reported.
The Shore News Beacon reported heavy police activity in the area about 10:20 a.m.
Around that time authorities alerted residents to shelter in place.
Eyewitnesses reported seeing police with guns drawn.
The suspect was allegedly seen carrying a rifle with a scope, according to the report.
The cemetery is located on Chesapeake City Road in New Castle County.
Reports say the shooting happened on cemetery grounds near a mausoleum.
A woman who works at the cemetery called her daughter and said two people were dead, but she didn’t know who they were.
Rich Barak of The Atlanta Journal-Constitution contributed to this report.