An initial sweep of the home by those SWAT members ended in three arrests.
But when regular police entered the home, they found two more suspects missed by the SWAT team.
Along with the suspension, the 12 SWAT team members will be re-trained.
SWAT teams swarmed a home in the city's South Chicago neighborhood after shots were fired at a police district commander late December 1. A five-hour standoff with the suspects ended early December 2.
In an emailed statement Thursday night, Chicago Police spokesman Anthony Guglielmi said: "SWAT is among the most highly trained, specialized unit within CPD and they are nationally recognized for their precision and tactical execution of high-valued operations. The officers received appropriate discipline for their actions and the Special Functions Division will ensure appropriate retraining for officers."
Police said several weapons were recovered from the scene.
A commander was checking out a suspicious person in an alley in the 8800-block of South Saginaw Avenue around 10:20 p.m. December 1 when one or more people opened fire on his unmarked patrol car, police said.
"I couldn't understand what was going on. I was surprised and kind of frightened. I didn't want to get in the window too much because I didn't want any stray bullets," said Debra Johnson, who lives nearby.
The commander saw at least one suspect run into a nearby home. A SWAT team and dozens of law enforcement agents were called to the scene after they refused to come out, police said.
Johnson said about five hours later, she heard a big boom.
"Then I just saw them take a couple of people and put them into squad cars," Johnson said.
Police said no one was hurt.
"I said there's something serious going on if the whole city out here. All the vehicles was out here earlier this morning. But it's shocking to know that that happened," said Caroline Bryant, a neighbor.
Chicago Police Superintendent Eddie Johnson said he will not stand by as his officers come under fire, and said the department will use the full force of the law against anyone targeting a police officer.
It was the third time in one week police have come under fire.
"Just by the grace of God they are all here to tell the story. That's ridiculous. Coming to work, doing their jobs, and they've been a target," Johnson said.
Among those arrested in the standoff was a repeat gun offender.
"We've got to change the culture in this city. We've got to change the mentality. We have to make it so gang members don't want to pick up a gun. That's what we're trying to get to," Johnson said.
Johnson used Jeremy Terry as an example of a repeat gun offender. Rather than jail, he was sent to a bootcamp.
"Gun offenders get a slap on the wrist in this city, and it has to stop. I need our judicial partners and state legislators to help me close this gap," he said.
After bootcamp, Johnson wants repeat gun offenders to get serious jail time. He said he is optimistic state lawmakers will take up the issue.