Officers were called to the Sainsbury's in Kidlington earlier this morning.
The 42-year-old victim has been taken to hospital where he is said to be in a stable condition.
Thames Valley Police tweeted about the incident earlier to say it happened at around 4am.
The post added, 'it is believed he sustained stab wounds.'
One person has been arrested and is in Police custody.
A scene-watch outside Sainsbury's has now been lifted.