Firefighters were called to Netto in Huddersfield Road, at 1200 BST.
Two different chemicals had mixed together, causing fumes and an odour, the fire service said.
"With chemicals you never know how they are going to react. They could have been very volatile," crew commander Tony Lander said.
It is not known what the chemicals were, but it is understood the two people had stopped at the supermarket on their way to taking the container for disposal.
The pair inhaled the fumes and were taken to hospital as a precaution, Mr Lander said.
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