Other official visitors with Trump, who did put on safety glasses for his tour, also were not wearing masks.
But Honeywell employees working on the production line were wearing masks. And a sign in the factory said that everyone there is required to wear a mask.
At one point during his tour, the Guns N' Roses cover of the James Bond movie song "Live and Let Die" was being blasted from the factory's PA system, as workers performed their tasks.
Trump, who has consistently refused to wear a mask while interacting with others despite federal guidance urging all Americans to do so, earlier Tuesday had said that he would put on a mask if it was required at the Honeywell facility.
A White House official said that Honeywell had told the White House that Trump and other visitors did not need to wear masks.
"If it's a mask environment, I would certainly do that," Trump had said Tuesday before boarding Air Force One to fly to Arizona.
"I would wear it. If it's a mask environment, I would have no problem."
Trump was not wearing a mask when he walked off Air Force One after it landed in Arizona.
And the president did not wear a mask at a roundtable discussion about Covid-19 assistance to Native Americans, which took place before he toured the Honeywell plant, which is producing masks under a $27.4 million Defense Department contract.
Trump was presented with one of those masks, mounted on a plaque, during his visit.
After his tour, Trump addressed workers, and lauded what he called the "incredible patriotic and hardworking men and women of Honeywell."
"Moments ago we saw the brand-new production lines where you're making high quality n95 respirators, they are made to perfection," Trump said. "There's no bad masks, like various countries have been sending. Bad masks from other places. Nothing like that at Honeywell."
"Respirators are there to protect our heroic doctors and nurses as they fight the unseen enemy. More than 150 Honeywell employees are working around the clock, three shifts a day six days a week. "
Trump's visit to Arizona was one of the few times in the past six weeks that he has left the White House. The president spent last weekend at Camp David.
Trump on March 28 had visited Norfolk, Virginia, to see off the U.S. Navy hospital ship Comfort, which sailed to New York City to alleviate strain on hospitals dealing with Covid-19 patients.
Vice President Mike Pence was criticized last week for not wearing a mask while touring the Mayo Clinic, despite that renowned health-care facility mandating masks for all visitors, patients and staff to prevent coronavirus infections there.
Pence did wear a mask two day later, when he visited a General Motors plant in Indiana that is manufacturing ventilators to meet demand from hospitals treating patients with Covid-19.
During a roundtable discussion Tuesday at Honeywell, Trump said it was time for the United States, which has drastically reduced the level of business and social activity, to start to reopen.
"We need to reopen our country," the president said. "We have a great country. We can't keep it closed."
He said the winding down of the White House coronavirus task force was warranted "because we can't keep our country closed for the next five years."
"The people aren't going to accept it, they don't accept it and they shouldn't accept it," he added.