The move on Thursday came two days after Trump warned North Korean leader Kim Jong-un in his address at the UN General Assembly that the US, if threatened, would "totally destroy" his country of 26 million people.
Announcing the executive order, Trump said the measure would allow sanctions against "individuals and companies that finance and facilitate trade" with Pyongyang.
"Our executive order will cut off sources of revenue that fund North Korea's efforts to develop the deadliest weapons known to humankind," he added.
Industries set to be targeted include textiles, fishing, information technology and manufacturing.
Pyongyang has resisted international pressure, conducting its sixth and largest nuclear test on September 3, and launching numerous missiles this year, including two intercontinental ballistic missiles and two other rockets that flew over Japan.
Trump stopped short of going after North Korea's biggest trading partner, China, and praised its central bank for ordering Chinese banks to stop doing business with North Korea.
He also did not mention Pyongyang's oil trade. Four sources told Reuters that China's central bank had told banks to strictly implement United Nations sanctions against North Korea.
Richard Gowan, non-resident fellow at New York University's Center on International Cooperation, said that China would find Trump's move "irritating" and would "respond by calling on the US to open a dialogue" with North Korea.
"China argues that it is worth putting sanctions on Pyongyang, but that should be balanced by some effort at negotiation, which the Trump administration has so far largely avoided," he told Al Jazeera.
'New EU sanctions'
The United Nations Security Council has unanimously imposed nine rounds of sanctions on North Korea since 2006, the latest earlier in September capping fuel supplies.
Also on Thursday, diplomatic sources told AFP news agency that the European Union had agreed on new sanctions against North Korea, including a ban on investments in the country and on EU exports of oil.
Speaking on condition of anonymity, the sources said that EU members also want to blacklist more North Korean individuals and entities, a move that would freeze their assets in the bloc and ban them from entering its territory.
"It seems, perhaps, that the US and EU measures have been coordinated," Al Jazeera's James Bays, reporting from the UN headquarters in New York, said.
"If that [EU sanctions]comes into play as well. It is even more pressure on North Korea, adding to all the existing international sanctions."
Earlier on Thursday, South Korean President Moon Jae-in, sitting with Trump and their respective delegations, said the US president's warning to Pyongyang on Tuesday "will also help to change North Korea".
It was Trump's most direct military threat to attack North Korea and his latest expression of concern about Pyongyang's repeated launching of ballistic missiles over Japan and underground nuclear tests.
In response, North Korea's foreign minister likened Trump to a "barking dog".
Arriving in New York for the UN meetings on Wednesday, Ri Yong-ho, the North Korean foreign minister, was mobbed with questions from reporters about Trump's maiden speech at the speech and he replied with a proverb.
"There is a saying that marching goes on even when dogs bark," he said as he entered his hotel.
"If they are trying to shock us with the sound of a dog's bark they are clearly having a dog dream."
On Thursday, South Korea's Moon said sanctions were needed to bring Pyongyang to the negotiating table and force it to give up its nuclear weapons, but Seoul was not seeking North Korea's collapse.
"All of our endeavours are to prevent war from breaking out and maintain peace," Moon said in his speech to the UN General Assembly.
He added that Pyongyang's nuclear issue "needs to be managed stably so that tensions will not become overly intensified and accidental military clashes will not destroy peace."
Moon said all countries must strictly adhere to UN sanctions on North Korea and impose tougher steps in the event of new provocations by Pyongyang.
Source: Al Jazeera and news agencies