The Royals had initially been hopeful of Tanvir being available for their entire group programme as a late replacement for Pakistan spinner Saeed Ajmal.
But problems started when he was drafted in as a replacement for his country's one-day series in Sri Lanka. It led to Tanvir having to return to Pakistan while Worcestershire attempted to solve the visa issue and, with four group games left, the county have opted not to pursue the issue.
Worcestershire chief executive David Leatherdale said: "It has been well documented that obtaining visas for overseas professionals is becoming more and more difficult.
"We are very disappointed that Sohail won't be joining us.
"But with just four group matches remaining, and still no guarantee that the visa process has been completed in Pakistan, his stay with the club is no longer practical.
"We thank Sohail for his efforts in doing everything he could in order to obtain his visa and wish him every success in the future."
It means that Worcestershire have only one overseas player for their T20 programme in Australian opener Phil Hughes.
But they are still on course to qualify for the quarter-finals after winning four of their opening six group encounters.