Officers were called to the area of the supermarket on Bowring Road earlier this afternoon following a report that a man had been assaulted.
The injured man required hospital treatment, but the Isle of Man Constabulary later confirmed his injuries are not life threatening.
Police said both uniformed officers and specially trained firearms officers were deployed as part of the response.
The force said the incident was resolved safely, with two people arrested.
In an update issued on Saturday evening, a spokesperson for the constabulary said it was aware that videos are circulating on social media showing part of the arrest on a bus travelling from Ramsey to Douglas.

The spokesperson said: ‘We recognise that the footage may cause concern, however, we would like to reassure the community that there is no ongoing risk, as well as take the opportunity to thank passengers for their cooperation in allowing the officers to safely work.’
The police are now appealing for appealing for any witnesses who may have seen the assault near Tesco to come forward.
Police are also asking for any passengers who were travelling on the bus where part of the arrest took place to assist with enquiries.
The spokesperson added: ‘Anyone with dashcam or other video footage relevant to the incident is also asked to contact us to help establish the full circumstances.
‘We respectfully ask the public to avoid speculation while the investigation remains ongoing.’
Tesco in Ramsey remains closed this evening (Saturday) due to police activity in the car park.

Officers said a further update would be provided as soon as possible and confirmed that there will continue to be a police presence in the area to support the investigation and provide reassurance.
Anyone with information is asked to contact the Isle of Man Constabulary on 01624 631212. Information can also be provided anonymously via Crimestoppers on 0800 555 111.
Earlier on Saturday, police confirmed they were dealing with what was described as a serious incident in the Tesco car park.
At that stage, the store was not accessible to the public while enquiries were ongoing.
Members of the public were asked not to attend the area.
Eyewitnesses reported seeing armed police in the area, with the car park cordoned off.
In a later update, officers confirmed the incident was isolated and that two suspects were in custody assisting with enquiries.
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