Authorities say Mohammad Youssuf Abdulazeez
, 24, also wounded three others when he sprayed a military recruiting center at a strip mall with bullets, then drove seven miles to assault Navy Operational Support Center Chattanooga before he was shot and killed by police.
Trump tweeted that the zones prevent soldiers from being able to protect themselves.
"Military Lives Matter! End gun free zones! Our soldiers must be able to protect themselves! This has to stop!" he tweeted.
Other 2016 candidates weighed in on the shooting Friday.
Jeb Bush echoed Trump's thoughts, telling reporters laws should be reviewed to allow military members working on bases and recruiting offices to carry guns.
"It seems to me that if you have military bases or recruiting offices, these are symbols of American might," he said during a campaign event in Carson City, Nevada. "They're targets. This is how you garner attention. You go to places where there is vulnerability and it's a very powerful symbolic attack on our country."
Bush said the Marines' deaths should motivate lawmakers to improve security.
"If the Marines were armed ... I think people would have known that, and had they known that, maybe they wouldn't have come in. Who knows?" he said. "I think it ought to be reviewed, for sure."
New Jersey Gov. Chris Christie said arming military personnel in recruitment centers needs to be considered.
"I don't know that there's any reason not to," Christie said at a diner in Milford, New Hampshire. "These are men and women who are trained in the use of firearms, they are some of the best trained people in the world on the use of firearms, so there should be, in my mind, no reason why they shouldn't be able to protect themselves. And I think after yesterday that's something that we should all consider and probably something we should thought of before."
Christie added that, if elected president, he would enforce existing federal gun laws more forcefully.
Wisconsin Gov. Scott Walker began an event in Davenport, Iowa, with a prayer, the Quad-City Times of Davenport reported
. Walker eventually prayed with a tearful veteran before leaving the event.
Their comments joined candidates who condemned the shooting hours after it happened on Thursday.
Lindsey Graham, an Air Force Reserve veteran, tweeted that his "thoughts and prayers go out to the families of the four Marines who were killed in today's horrific attack."
Meanwhile, Democratic frontrunner Hillary Clinton called the incident "an act of domestic terrorism."
"It's terrible when we lose Marines anywhere in the world, but to lose four in Chattanooga, Tennessee, is just heartbreaking," Clinton said at a campaign event in New Hampshire.