The match makes the third round of this season's top flight after the first two matches for each of the competitors had climaxed.
Polisi Tanzania is leading the league after coming out victorious in two fixtures and accumulating six points.
The Kilimanjaro-based outfit got off to a good start, trouncing Dar es Salaam's Kinondoni Municipal Council FC 2-0 in Karatu, Arusha.
In the second match, the law enforcers put solid showing to notch a vital 2-1 win over one of the league big guns, Azam FC, in Kilimanjaro.
Simba SC sits sixth with four points after settling for the draw in one tie and winning one.
The league big guns were held to a 0-0 draw by Mara's Biashara United in Musoma and thereafter post slim 1-0 win over Dodoma Jiji FC in Dodoma.
A statement from the Tanzania Premier League Board (TPLB) which was made public yesterday stated that the match between Simba SC and Polisi Tanzania will not be played on October 20 as Simba SC is set to battle it out in this season's CAF Champions League first round this weekend.
The Tanzania envoys in the premier continental competition will confront Jwaneng Galaxy of Botswana in Gaborone on October 17.
The Simba SC vs Polisi Tanzania tie will as a result take place on October 27 at the same venue, with Simba hosting it.
The reason for the postponement of the top-flight match is said to be Simba facing the challenge of getting transport at the right time back to the country from Botswana, where they will play the Botswana top-flight champions.
Simba, one of the previous season's CAF Champions League quarterfinalists, is set to travel to Gaborone today.
The squad is the only Tanzanian side in this season's continental competition after compatriots Yanga was knocked out by Nigeria's Rivers United FC in the preliminary round last month.