At around 11.30am today, officers attended a house on Wick Road, Wick St Lawrence, as part of an investigation into possible firearms offences.
A man inside the property was subsequently shot by police.
Officers immediately provided the man, who is aged in his 30s, with first aid before he was then taken to Southmead Hospital where he remains in a critical but stable condition.
His next of kin have been informed and are being kept fully updated.
A cordon is in place on Wick Road while enquiries are carried out at the scene.
Chief Inspector Adam O’Loughlin said: “We understand the local community will be shocked and people will want to know what happened.
“As someone has been injured, we have referred this to the Independent Office for Police Conduct which has confirmed it will carry out an independent investigation.
“We are committed to being open and transparent and will fully cooperate with the IOPC.
“Our thoughts are with the man and his family as he continues to receive treatment at hospital.
“Anyone with concerns about this incident is encouraged to speak to officers at the scene or contact their local neighbourhood team.”