Nagelsmann, whose sacking in March 2023 led to Tuchel's arrival, was tipped to return to Bayern, but has now extended his contract with Germany until 2026
The France international Griezmann protested after being booked for diving by Juan Martinez Munuera.
Atletico have 10 working days to appeal against the ban, Spanish football federation RFEF said in a statement.
The RFEF also confirmed a one-game ban against Real Madrid defender Sergio Ramos for being sent off in his side’s 3-0 win at Deportivo La Coruna.