At 09:43 GMT Barclays was trading down 1.15%, HSBC Holdings was down 1.50%, while shares in Royal Bank of Scotland Group had fallen 0.42%.
The Dow Jones Euro Stoxx Chemicals index at 09:46 GMT was trading down 2.42%, as shares in many of Europe's major chemical companies fell.
Top European producers were hit hard-petrochemical major BASF's shares had dropped 2.85%, while fellow Germany-based Bayer had fallen 3.22%. Dutch coatings firm AkzoNobel was down 2.44%, and France‘s Arkema had fallen by 1.67%.
Belgium's Solvay had fallen 3.65%, France-based industrial gases company Air Liquide was down 3.16%, while Germany's Linde was down 1.29%. Catalysts maker and precious metals trader Johnson Matthey of the UK was down by 1.46% and Swiss specialties maker Clariant was trading down 2.49%.
At 09:53 GMT, the UK's FTSE 100 had slumped by 2.00%, Germany's DAX was down by 2.79%, and the CAC 40 in France had fallen 3.66%.
Asian petrochemical shares also dropped on Monday on renewed concerns on the sovereign debt crisis in the eurozone and its dampening impact on global demand.
Japan's benchmark Nikkei 225 index was down by 2.31% at closing. Financial markets in South Korea, China and Taiwan are closed on Monday for holidays.
