The Pierce County Sheriff's Office said the unidentified man was cornered in a residence in the Fife Heights neighborhood about 4:30 p.m., The Seattle Times reported.
"The gunman is contained inside his residence," sheriff's department spokesman Ed Troyer told The (Tacoma) News Tribune.
"He is believed to be armed with multiple firearms and is refusing to come out or to put down his weapons. The SWAT team is en route."
Before he entered the home, the gunman had fired indiscriminately at other residences and it wasn't known whether anyone had been shot, the Times said.
Residents were advised to stay indoors.
"This is a very dangerous situation," the sheriff's office said in a statement.