Japan's Nikkei 225 index has plunged 2.5 percent Monday to 9,142.47. Hong Kong's Hang Seng tumbled 2.5 percent to 20,564.87. South Korea's Kospi shed 1.7 percent.
In Greece, which has been battling a severe debt crisis for more than two years, no political party won enough votes to form a government.
In France, President Nicolas Sarkozy lost to Socialist candidate Francois Hollande, who had criticized the country's austerity program and wants to boost government spending.
On Friday, U.S. stocks plunged after the government reported that hiring slowed sharply in April.