Vladimir Lekic was arrested on an Interpol warrant at his home in the Montenegrin town of Cetinje.
Police said Lekic was suspected of taking part in a robbery in Frankfurt, Germany, in December 2003, when watches worth about $1.4m were stolen from a jewellery store.
Lekic allegedly carried out the robbery together with two fellow Montenegrins, who are already in jail in France, police said.
The police statement said that Germany would allow Montenegro to try Lekic. Local laws in Montenegro do not allow for the extradition of Montenegrin citizens.
The Pink Panthers are believed to be mainly from countries in the Balkans. They are the prime suspects in a series of jewel thefts worth over $150m over the past decade in Europe, Asia and the Persian Gulf.
They are suspected of carrying out a robbery shortly before Christmas at the glamorous Harry Winston jewellery shop on one of Paris' fanciest streets. Thieves walked into the store and made off with jewels worth $108m.
Some Pink Panther members already are serving time in jail. Three Serbs were convicted in 2005 for a robbery in Japan, which included a necklace worth $27m.