Flames and smoke were seen billowing into the sky at the site in the town of Moerdijk, near the port city of Rotterdam.
A spokesman for the company said maintenance was being carried out at the complex at the time of the explosion.
"An explosion occurred on the evening of 3 June in the reactor of the MSPO-2 installation at Shell (LSE: RDSB.L - news) 's Moerdijk chemicals complex in the Netherlands," the company said in a statement.
"A fire broke out as a result. The fire is now under control. The authorities and emergency services were alerted immediately.
"Emergency services are on site. Two employees were injured and have been taken to hospital for treatment.
"The MSPO-2 installation was under maintenance as the fire broke. The plant produces styrene monomer and propylene oxides which are raw materials used to make plastics."
Residents who live close to the site were told to close their doors and windows to avoid the plume of smoke.
Firefighters used foam to battle the fire.