The chairman of leading Greek lender National Bank, Rapanos was taken to a private hospital in Athens, a government spokesman said, hours before he was expected to take his oath of office.
The hospital said Rapanos was brought in with "strong stomach pains, vertigo, nausea, sweating and fatigue."
Doctors have stabilized his condition and he is undergoing tests.
The state-run Athens News Agency said Rapanos had run a high fever while at his office at National Bank ahead of his swearing-in ceremony.
A former economics professor who served in the economy ministry when Greece joined the euro in 2001, Rapanos was named finance minister on Thursday in a conservative-led coalition seeking to revise the country's bailout terms.
Newly-elected Prime Minister Antonis Samaras was briefly in another Athens hospital Friday after being diagnosed with a retinal detachment.
He returned to his office according to state television, but will be admitted on Saturday to undergo an operation.
As a result, Samaras will be unable to attend his country's Euro 2012 quarter-final game against Germany later on Friday.
He also cancelled his party's first parliamentary meeting.
The coalition government, backed by conservative, socialist and moderate leftist parties, is under intense international pressure to implement the terms of an EU-IMF bailout package that has kept the indebted country's economy afloat for two years.
Pressure is mounting in view of Monday's upcoming visit of European Commission, IMF and European Central Bank inspectors, who return to Athens to resume discussions suspended because of Greece's two-month political deadlock.
Incoming Greek finance minister Vassilis Rapanos, National Bank, Athens News Agency, Prime Minister Antonis Samaras, government spokesman, finance minister, Rapanos, Athens, coalition government