The name of the trooper has not been released pending notification of family.
Video from the Action Cam at the scene in Bear, Del.
The barricade situation was happening in a home on the 500 block of St. Michaels Drive in the Brick Mill Farms Development in Middletown.
Police said the male suspect is refusing orders to surrender and has fired shots at officers.
It is believed that he is inside the home by himself. Hostage negotiators were trying to establish contact with the man.
A heavy police presence could be seen from helicopter footage from ABC7's sister station, WPVI-TV.
Video: Chopper 6 over search for suspect in Middletown, Del.
Residents in the area were told to stay inside their homes and lock their doors until notified otherwise.
The trooper was shot around 12 p.m. at the Wawa store on Pulaski Highway (Route 40) near Salem Church Road.
Officials said the trooper spotted a suspicious vehicle occupied by two suspects in the Wawa parking lot.
The trooper made contact, and then there was a struggle, officials said.
That's when one of the two suspects got out of the vehicle and fired several rounds, striking the trooper.
Video: Del. state police news conference on trooper's death
Responding troopers arrived at the scene and took one of the suspects into custody without incident. The other suspect fled on foot prior to their arrival.
The trooper was rushed to an area hospital, where he succumbed to his injuries.
"This is a sad day for our state and our Delaware State Police family. We ask that you keep the trooper's family, and the Delaware State Police family, in your thoughts and prayers," said Delaware State Police Superintendent Nathaniel McQueen.
Meanwhile, a lockdown was lifted for the Appoquinimink School District in the Middletown, Delaware area. Those schools had been locked down amid the search for the shooting suspect.