The French club, scheduled to play the match on Saturday (AEDT), withdrew because coronavirus "sanitary conditions were not met", despite organisers being "satisfied" it was safe to play the game.
The match was set to be the first of this weekend's second round of matches.
"The Rugby Club Toulonais learned this Thursday, 18 December (AEDT), that at least one player from Scarlets had tested positive for COVID-19 at the start of the week," a statement from the Top 14 club read.
"Although aware of the serious consequences, we decided not to play this match as planned..."
This is the first voluntary forfeit by a club in the competition, after organisers cancelled three other games this week – Toulouse v Exeter, Glasgow v Lyon and La Rochelle v Bath – because of COVID-19 cases at the British teams.
Organisers EPCR said the player in question self-isolated and that two others were left out of the Scarlets squad.
"The (Scarlets) player self-isolated in accordance with public health guidelines and his two close contacts were not selected in the matchday squad," an EPCR statement read.
"A medical risk assessment committee was convened earlier today (Friday) to consider any potential issues in relation to Scarlets' testing and tracing, and it was satisfied that the risk of further transmission had been contained before recommending that the match could go ahead safely."
Toulon was also given the option of playing later in the weekend instead, but turned it down.
"It was suggested that the match could be postponed to a later date in the weekend to allow any of the club's players to opt out of the match if they wished to do so," EPCR added.
"It was also suggested that RC Toulon could source willing players from their existing tournament squad to replace those who had withdrawn and that the Scarlets matchday squad could undergo additional PCR testing.
"These offers were rejected by RC Toulon, and EPCR can therefore confirm that the match is postponed."
The outcome of the other cancelled matches will be decided by a committee, with 28-0 wins on the cards for the French sides.