Tory vice-chairman Alan Lewis, 75, who was appointed by David Cameron, was held by police after a woman claimed she was attacked in the late 1960s.
The self-made tycoon, who owns the Crombie clothing chain and is thought to have a fortune of between £220-260 million, was reportedly arrested at a Manchester hotel while on a business trip.
A Greater Manchester Police spokesman said: "A 75-year-old man was arrested following a complaint received earlier this year of an historic rape that occurred in the Manchester area in the late 60s.
"The man was later bailed pending further inquiries. Specially-trained officers are providing support and welfare to the victim."
The Prime Minister gave Mr Lewis his current role as Tory vice-chairman responsible for business relations in 2010.
Crombie was originally set up in 1805 and was famously associated with Grandholm Mill on the banks of the River Don in Aberdeen.
The company became part of Illingworth Morris after World War Two and was taken private by Mr Lewis in 1983. Production ceased at Grandholm in 1990.
That same year, Mr Lewis was made a CBE for his services as chairman of the Confederation of British Industry's initiative to prepare British businesses for the single market.
A Tory supporter since the early 1980s, he is a black belt in karate and a promoter of Christian healing who claims to read the Bible every day.
Update: The Crown Prosecution Service in England has now decided not to take any further action.
A spokesman said: "The CPS has carefully considered the evidence gathered by Greater Manchester Police in relation to their investigations into an allegation of rape in the Manchester area in 1967.
"The case has been reviewed by two specialist rape prosecutors in CPS North West Area in accordance with the Code for Crown Prosecutors, the CPS policy for prosecuting cases of rape and CPS legal guidance on rape and sexual offences.
"We have concluded that there is insufficient evidence for a realistic prospect of conviction in relation to the allegation and have advised Greater Manchester Police that no further action should be taken.
"The complainant has been informed of the decision and we will be meeting her to provide an explanation of the decision and to answer any questions she may have."