Jamal Musiala grabbed a brace while Malik Tillman, Leroy Sane, Michael Cuisance, Bouna Sarr and Corentin Tolisso were also on target as Julian Nagelsmann’s side eased through to the second round of the competition.
On top of his four goals, Choupo-Moting also provided assists for Musiala and Sarr on a miserable day for fifth-tier Bremer, who had Ugo Nubile sent off later on.
For Bayern, it was the second-highest margin of victory in their history after a 16-1 thrashing of Waldberg in 1997.
Though much-changed by Nagelsmann, Bayern never looked in danger of suffering only a second defeat in 24 competitive matches against sides below Germany's top three divisions.
Just eight minutes had passed when Sane's cutback was fired in off the underside of the crossbar by Choupo-Moting, who turned provider in the 16th minute with a neat lay-off for Musiala to slot home.
That same combination unlocked Bremer once more 11 minutes later, with Jan-Luca Warm turning Musiala's shot over his own goal line.
Choupo-Moting tapped in his second as the hosts were caught out from the subsequent kick-off, before completing his hat-trick with a 35th-minute header from close range.
Bayern picked up from where they left off with two goals within three minutes of the restart. Substitute Tillman pounced on poor play before slotting home, while Musiala rifled in his second less than 60 seconds later.
Sane got in on the act in the 65th minute, before Nobile was sent off for dragging back Tillman as he raced into the box.
Four goals followed in the final 10 minutes. Cuisance and Choupo-Moting took the visitors' tally into double figures, while further strikes from Sarr and Tolisso completed the rout.