The 41-year-old, who served under ousted pro-Kremlin president Viktor Yanukovych, was arrested in Altea, a hilltop village on the Mediterranean coast, the source said.
He is the first minister from Yanukovych's adminstration to be detained.
A court in Kiev issued a warrant for his arrest in January at the request of the prosecutor general's office.
Ukrainian prosecutors accuse Kolobov, along with Yanukovych and Ukraine's former prime minister Mykola Azarov, of misappropriation of over 220 million hryvnia($8.5 million/€7.6 million) in public funds.
According to an arrest warrant issued by Interpol, he is wanted for misappropriation and embezzlement.
Kolobov, a former deputy head of Ukraine's central bank, was appointed finance minister in 2012 by Yanukovych, who was toppled in February 2014.
Yanukovych fled to Russia after months of protests in Kiev against his decision to back away from an EU association deal and instead seek close ties with Ukraine's former master Moscow.
The current pro-Western leaders accuse Yanukovych and a coterie of relatives and close allies of accumulating huge wealth by robbing state coffers and plundering national assets through corrupt deals.
Yanukovych has denied that he or members of his family were involved in corruption.
After he fled Ukraine, Russia said Yanukovych had been the victim of a "fascist" coup and went on to annex Ukraine's Crimean peninsula.
In a confrontation with Kiev's current pro-Western leadership, Russia has supported separatists in Ukraine's predominantly Russian-speaking industrialised east though Moscow denies its forces have been involved in fighting.
The conflict has killed at least 5,800 people since April and has dragged ties between Russia and the West to their lowest since the Cold War.