Tehran prosecutor Ali Alqasimehr said Mr Trump and 35 others faced murder and terrorism charges, and that Interpol had been asked to help detain them.
However, Interpol said it would not consider the Iranian request.
The US special representative for Iran said the warrant was a propaganda stunt that nobody would take seriously.
Soleimani died in a drone strike near Baghdad International Airport ordered by Mr Trump, who said the general was responsible for the deaths of hundreds of American troops and was planning imminent attacks.
Iran retaliated by firing ballistic missiles at Iraqi military bases housing US forces.
"About 36 individuals have been identified in connection with the assassination of Hajj Qasem. They supervised, acted upon, and ordered [it]," Mr Alqasimehr was quoted as saying by the Mehr news agency.
"This includes political and military officials from the US as well as other countries, for whom the judiciary has issued arrest warrants and the Interpol has issued Red Notices."
Mr Trump was on the top of the list and his arrest would be sought even after his presidency had ended, the prosecutor added.
Trump: 'We took action to stop, not start a war'
UN expert: Soleimani killing breached international norms
What does the law say about Soleimani's assassination?
Deputy Foreign Minister Mohsen Baharvand said Iran's judiciary would soon issue an indictment for those responsible for the attack on Gen Soleimani, and was hoping to identify the operators of the drone, according to the Isna news agency.
"Iran will not stop its efforts until these people are brought to justice," he declared.
An Interpol Red Notice is a request to law enforcement worldwide to locate and provisionally arrest a person pending extradition, surrender, or similar legal action. It is not an international arrest warrant.
US special representative Brian Hook said: "Our assessment is that Interpol does not intervene and issue Red Notices that are based on a political nature.
"This is a political nature. This has nothing to do with national security, international peace or promoting stability... It is a propaganda stunt that no-one takes seriously."
Interpol, which is based in the French city of Lyon, subsequently told the BBC that it would not consider the Iranian request for help.
Under its constitution, it was "strictly forbidden for the organisation to undertake any intervention or activities of a political, military, religious or racial character", it said.
Analysts say the issuing of the arrest warrant is little more than a symbolic gesture by Iran, but that it reflects the depth of animosity felt towards President Trump.