The France international turned 30 on Sunday and his teammates had planned to throw the attacker a surprise party at Italian restaurant Hugo's in the evening.
Captain Philipp Lahm informed the club about the team's plans in advance, as is customary for these kinds of events, yet Sammer and Heynckes decided against giving permission as they want Bayern to focus on the second leg of the quarterfinal tie against Juventus instead.
The Bavarians already kept celebrations to a minimum after they secured the Bundesliga title at the weekend and they are wary of any distractions ahead of Wednesday's match in Turin.
"Postponing any celebrations also characterizes a champion. It's a pleasure, but we cannot afford to get ahead of ourselves," Sammer told Bild.
"Juventus won the Serie A title in 1997 and then celebrated their success. Borussia Dortmund would not have won the Champions League otherwise."
Bayern will defend a 2-0 lead from the first leg at the Juventus Stadium.
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