The Abahani skipper reached the landmark on his way to 55 against Gazi Group Cricketers at BKSP-3 on Tuesday, reports bdnews24.com.
Asked to bat first, Tamim opened the innings 38 runs shy of the milestone.
He hit Saeed Anwar Junior for back-to-back boundaries in the 18th over to become the first Bangladeshi to sign into the 6,000-run club - in 187 List A innings that included eight centuries and 41 fifties.
Tamim has 4,713 runs in One-Days; 4,899 in the national team List As including warm-ups.
The 27-year-old has notched 326 runs in eight matches in the league this year.
His national teammate Mushfiqur Rahim, the captain of Mohammedan Sporting Club, also had the opportunity to reach the milestone on Tuesday.
But the Test skipper, who needed 97 runs to join Tamim, got out for a duck against Prime Bank in Mirpur.
Ace all-rounder Shakib Al Hasan has 5,276 runs in List A cricket.