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.
Officers are currently in the car park of Sainsbury’s, Kidlington after a man was found seriously injured there at about 4am today.— TVP_Kidlington (@TVP_Kidlington) January 15, 2020
It is believed he sustained stab wounds. One person has been arrested and is in custody.
People are asked to avoid the area. pic.twitter.com/893xmVOBNA