Karpela and her two children will spend three weeks doing volunteer work at the ashram beginning in late December.
Karpela met with Amma during a recent visit to Finland, and is the honorary chair of the Finnish Amma organisation.
Karpela, whose portfolio includes religious affairs, defended her visit to YLE TV news on Saturday. She said that her interest in Amma's teachings does not contradict her own Evangelical Lutheran faith, and stressed the importance of tolerance in spiritual matters.
The Evangelical Lutheran and Greek Orthodox churches are state-supported churches in Finland.
In an open letter to the tabloid newspaper Ilta-Sanomat, Karpela denied that Amma's group is a cult or sect, likening the leader to Mother Teresa.
A former Miss Finland, the 34-year-old Karpela was elected to Parliament on the Centre Party ticket in 1999. She became Minister of Culture in the spring of 2003. She has also made headlines this year with a brief engagement to former Conservative Party chair and Finance Minister Sauli Niinistö.