He told "Power Lunch" Trump's move "undercuts every American president" since President Harry Truman, who all understood that the U.S. is the most likely mediator in a peace deal between the Israelis and Palestinians.
The status of Jerusalem — home to sites holy to the Muslim, Jewish and Christian religions — is one of the thorniest obstacles to reaching a peace deal between Israel and the Palestinians.
Israel considers the city its capital and Palestinians want the capital of an independent Palestinian state to be in the city's eastern sector.
"President Trump is now taking sides," Burns said.
He believes that will diminish American credibility among the world's 1.6 billion Muslims.
He's also concerned it may inflame passions against the U.S.
There are also no peace negotiations underway right now, Burns pointed out.
"The president offered this major American concession of 70 years that no one else was willing to make and he appears to have gotten nothing in return," he said. "We have to worry about America's interest here and if you offer a major concession and get nothing in return, then I think you really harmed the United States."
In his announcement, Trump said his decision "is not intended in any way" to hamper a peace agreement.
However, the move has angered leaders across the Middle East, who have voiced concerns about the impact on future peace talks and further destabilization of the region.
Sarah Stern, president of the pro-Israel Endowment for Middle East Truth, hailed Trump's decision.
"This is long overdue," she said in an interview with "Power Lunch."
"We have diplomatic relations with 190 countries. They have all selected where they want to place their capital city, except for Israel," Stern added.
The White House did not immediately respond to a request for comment on Burns' remarks.
— Reuters contributed to this report.