Bayern, whose last encounter with Plzen was in 1971 with a 7-1 aggregate win, set a frantic early pace and European footballer of the year Ribery gave them a deserved 25th-minute lead with a spot kick.
David Alaba doubled it 12 minutes later with a low drive and Ribery got another with a superb chip in the second half. Bastian Schweinsteiger added a goal three minutes later and Mario Goetze completed the scoring in stoppage time.
The result gave leaders Bayern nine points, three ahead of Manchester City, who beat CSKA Moscow 2-1. Plzen are bottom of the table having lost their three games.
"We played a good game and it felt good coming back," Ribery told reporters, after missing last week's 4-1 Bundesliga win against Mainz with an ankle injury.
"We enjoyed ourselves out there but there are tough games ahead so we need to win at Plzen in our next match."
It was always going to be a one-sided affair, with the entire Plzen team worth about as much as Bayern midfielder Xherdan Shaqiri, and the hosts made their intentions clear early on.
"We played well from the start and I have realised how special this competition is for the team and the whole club," coach Pep Guardiola told reporters.
"It was a good performance and I am satisfied but we can always, always, always play better," said the Spaniard, whose team is still unbeaten in the league, Champions League and German Cup.
Plzen keeper Matus Kozacik twice let the ball slip through his hands in the opening minutes as Bayern pressed for an early goal.
Arjen Robben almost got it but his sliding effort went just wide in the sixth minute with the Czechs in disarray.
Kozacik was kept busy and did well to save shots from Ribery and Alaba as the Bavarian onslaught continued.
Ribery, who set a German record after having not been on the losing side for Bayern in 39 games, gave them a well-deserved lead with a penalty after Robben was brought down.
There was some controversy with the Dutchman, who was told not to take a penalty during the game against Mainz, refusing to take the spot kick despite Guardiola's loud orders.
"Arjen has a character and that's normal in football and this is Bayern," Ribery said. "The coach said Arjen but Arjen did not want to shoot."
Robben did not want to comment on the incident.
Alaba scored with a shot from just inside the box in the 37th minute as Bayern played cat-and-mouse with the bottom-placed Czechs.
Quickfire goals from Ribery, with a superb chip after shaking off two defenders in the box, and Schweinsteiger's fine turn in the box, followed in the second half, and substitute Goetze sealed the win from close range to end a nightmare evening for the Czechs.
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