Van der Voort was due to take on James Wade in a third-round clash at the Alexandra Palace, but Wade will now receive a bye into the last 16.
A statement said: "Vincent Van Der Voort has withdrawn from the William Hill World Darts Championship after testing positive for Covid-19 ahead of his match with James Wade.
"Wade will receive a bye to the last 16 and Monday evening's session will continue with two matches."
The 46-year-old is a popular figure among the darting community and has reached three world championship quarter-finals (one in the BDO and two in the PDC).
Following the announcement, Wade wrote on Twitter: "Wishing Vincent a speedy recovery! #WorldDartsChampionships."
Van Der Voort's fellow Dutchman Raymond Van Barneveld tested positive after beginning to feel unwell in the wake of his 3-1 defeat to Rob Cross on Thursday night.
On Sunday, following Van Barneveld's positive test, organisers insisted all necessary precautions were in place to safeguard both players and fans at the event.
A Professional Darts Corporation spokesperson told the PA news agency: "We have been made aware of Raymond's positive test and send him our best wishes for a speedy recovery.
"We are following approved protocols and have appropriate regulations in place around the William Hill World Darts Championship, one of which is that all players and staff must produce a negative Covid test result on their return to the event after the Christmas break."