The 46-year-old was last seen in the Cottage Mews area of Fordingbridge at around 5.20am this morning (Saturday 2 June).
Police have made a number of enquiries to locate him and are growing increasingly concerned for his welfare.
Officer are asking members of the public to keep an eye out for him and report any sightings to us.
Officers are also in the Westbourne area of Dorset making enquiries in relation to this investigation, so if you live in or near this area, please share our appeal.
Matthew is described as:
6ft 1ins tall
Light brown hair
Black rimmed glasses
If you have seen Matthew, or know where he is, please call police immediately on 101, quoting 44180205072.
Dial 999 in the event of an emergency.