The Bosnia-Herzegovina international, 24, was with a friend when officers stopped their car after a member of the public raised concerns. Reports said six police vehicles, including armed police, were sent to the area.
The pair were reportedly stopped in the Darras Hall area, around seven miles from where they had first been seen. Officers searched the vehicle and seized the bow and arrows, but were satisfied that neither man posed a threat to the public.
BBC Sport was told that Dedic had no ill intention and had fully co-operated with police.
It was also reported that Newcastle United goalkeeper Mark Gillespie, 34, and former defender Paul Dummett, 35, arrived while officers were speaking to Dedic. The pair are understood to have been in the area by chance and stopped to offer assistance.
The incident happened on Wednesday, two days after Dedic featured in Newcastle's 1-0 home defeat by Everton. He joined the club from Benfica in August for a fee reported to be in the region of £30 million and has made 10 league and cup appearances since his arrival.
Newcastle have not commented. Northumbria Police confirmed that enquiries were ongoing, although the force did not name Dedic in its statement.
The police said they had received reports of two men carrying a bow and arrows while walking along a track beside the reservoir on Military Road in the Harlow Hill area.
“Officers attended and subsequently stopped a vehicle in the Darras Hall area and seized a bow and arrows,” the statement said.
“At this stage, it is understood they were for recreational use and there was no threat to the public.”
Newcastle, who have collected 11 points from nine Premier League matches and sit 13th, are due to visit Fulham on Saturday before the November international break.
Dedic has been named in the Bosnia-Herzegovina squad for Nations League matches away to Sweden on November 14 and at home to Romania on November 17.