It was not clear what prompted the US ban but it is understood all foreign missions were aware of the British investigation.
Until now, such individuals were able to take advantage of "protocol services" where they did not have to physically appear at the US embassy to obtain a visa.
But on Thursday, US Ambassador Robert Jackson told members of parliament that the process had changed, sources in the legislature said.
"If you are travelling for tourism or business that is not related to government business, you will be required to make a personal appearance, even with former presidents," he said.
"There are no exceptions."
The withdrawal of protocol privileges comes two months after Britain's top diplomat in Accra accused three MPs and a former lawmaker of visa fraud in a letter to Ghana's parliament, raising the prospect of a travel ban.
The allegations included visa overstays for family members, in some cases for several years, after they used diplomatic channels for travel on non-official business.
Britain's outgoing high commissioner Jon Benjamin said MPs wanting to make private visits now had to apply "like any other applicant".
It was not clear what prompted the US ban but it is understood all foreign missions were aware of the British investigation into visa irregularities involving MPs.
Contacted by AFP, the US embassy in Accra gave no immediate response.
The US decision is not thought to be connected to a Ghanaian Supreme Court ruling on Thursday on two former Guantanamo Bay detainees.
The court ruled that the 2016 transfer of the pair from the US detention facility to live in Ghana was unconstitutional.