He would also not work for any foreign-owned companies if his father were elected, his lawyer said.
Mr Trump has called on China and Ukraine to investigate Joe Biden over his son’s activities in both countries, without any evidence of any wrongdoing.
The issue is central to an impeachment inquiry against the US president.
Mr Trump and his supporters have accused Joe Biden of abusing his power as vice-president to pressure Ukraine to back away from a criminal investigation that could have implicated his son who then worked for a Ukrainian energy company.
He has also accused Hunter, 49, of using his position of influence to get China to invest in a fund he was involved in.
The impeachment inquiry begun by opposition Democrats in the US House of Representatives centres on allegations that the president broke the law by soliciting help from a foreign power Ukraine for electoral gains.
A statement released through Hunter’s lawyer said he would resign by 31 October from the board of BHR Shanghai Equity Investment Fund Management Company.
It said he joined the board in an unpaid position “based on his interest in seeking ways to bring Chinese capital to international markets”.
The statement said Hunter would “readily comply” with guidelines issued by his father if he was elected president “to address purported conflicts of interest, or the appearance of such conflicts”, and would, “in any event”, agree not to serve on the boards of or work on behalf of foreign-owned companies.
The statement also detailed the nature of his work in Ukraine and China, stressing that there had been no wrongdoing.
Mr Trump has accused the former US vice-president and his son Hunter of corruption in their political and business dealings in Ukraine and China, without offering specific evidence.
When Hunter Biden joined the board of Ukrainian natural gas company Burisma in 2014, questions were raised about a potential conflict of interest for his father.
Ukraine was undergoing a political transition after its pro-Russia president was forced out of office, while the elder Biden was the Obama administration’s point man for the Eastern European country.
In 2016, Joe Biden pushed the Ukrainian government to fire its top prosecutor, whose office had been scrutinising the oligarch owner of Burisma.
In a speech last year at a think tank, Joe Biden boasted of having forced the prosecutor out by threatening to withhold a billion-dollar loan guarantee to Ukraine.
Mr Trump and his allies accuse Joe Biden of acting to protect his son. However, other Western officials and major financers of Ukraine’s government also wanted the prosecutor dismissed because he was seen as a barrier to anti-corruption efforts.
Trump attacks forced Hunter Biden to resign from board of a Chinese company.