He is expected to appear at the police headquarters on Thursday, June 13, 2019.
His arrest comes one week after the abduction of two Canadian women, who have been kidnapped in the country.
A statement from the police said: "The Criminal Investigation Department (CID) is investigating various acts of kidnapping and causing unlawful damage in which credible and actionable intelligence makes Mr. Samuel Ofosu-Ampofo, the National Chairman of the National Democratic Congress (NDC), a suspect."
The NDC Chairman was arrested in Accra after he refused to cooperate with police investigations, the statement said.
"Mr. Samuel Ofosu-Ampofo is currently in lawful police custody in respect of the ongoing investigations," police said, calling on the public to remain calm.
Kidnap rare in Ghana
Abductions and violent crime toward foreigners are rare in Ghana, but appear to be on the rise in recent months.
In April, an Indian man was abducted in Kumasi by an armed gang demanding a cash ransom. He was rescued by the police.
In the same month, a consular-general from Estonia was also reportedly kidnapped in the capital, Accra, but was also rescued by police.
The managers of Canada's diplomatic and consular relations, Global Affairs Canada (GAC) have confirmed that two Canadians have been kidnapped in Ghana.
The two Canadian women, according to reports were abducted at Kumasi in the Ashanti Region.
Between August 2018 and January 2019, three young women were kidnapped at Takoradi in the Western region.
However, nothing has since been heard after the police held a press conference that the missing girls have been found with parents of the kidnapped girls still soliciting answers from the police.