"The impact of negative oil means different things for different Asian economies - but if you have to generalize, it isn't great news," Robert Carnell, regional head of research, Asia-Pacific at ING, wrote in a note.
Such a big negative deviation from the optimal price of oil will likely weigh heavily on demand for Asia's exports, he added.
The Southeast Asia region experienced broad losses with Vietnam's main index settling 3.5% down - its lowest close since April 13 and worst day since March 30.
Vietcombank closed nearly 1% down after the commercial lender posted a 11.2% fall in first quarter profit.
The Philippines ended 2.5% lower, bogged down by industrials and consumer stocks.
Alliance Global Group declined 6.7% at close, while JG Summit tumbled 6.2%.
Malaysian stocks closed the session 2.2% down, its worst day since March 23.
Petronas Chemicals Group finished 7.3% lower, while Hartalega Holdings shed 5.5%.
Meanwhile, Singapore and Indonesia both closed about 1.6% lower. Singapore's Sembcorp Industries slid 4.4%, while Tourindo Guide Indonesia finished about 8% down.