Toffees boss Silva approached referee Lee Mason and his assistants on the pitch at St James' Park after watching the visitors throw away a two-goal lead.
The Portuguese was furious with the decision to let Ayoze Perez's late winner stand amid suspicions of offside.
Silva also claimed Gylfi Sigurdsson should have been awarded a penalty during the defeat, Everton's fourth loss in their last six games.
An FA statement read: "Marco Silva has been charged with a breach of FA Rule E3 following the Premier League game against Newcastle United on Saturday].
"It is alleged the Everton manager's behaviour on the field of play at the end of the fixture amounts to improper conduct. He has until 18:00 [GMT] on Thursday [14 March 2019] to respond to the charge."
However, Newcastle manager Rafa Benitez could have been excused for feeling similarly aggrieved despite the win, after goalkeeper Jordan Pickford avoided a red card for hauling Salomon Rondon to the ground, before saving Matt Ritchie's subsequent penalty with the score 1-0 to the Toffees.
Just over a minute after the Englishman's save, Everton doubled their lead through Richarlison at the other end.
The Magpies staged a terrific second-half fightback, though, as Rondon gave them a lifeline before Perez netted twice to complete the turnaround, leading to Silva's enraged outburst that followed the full-time whistle.
If the former Watford boss fails to successfully appeal the charge, he could be handed a touchline ban similar to the one Tottenham manager Mauricio Pochettino received following a similarly heated on-pitch exchange with referee Mike Dean in February, forcing him to the stands for his next two games.
Assuming Silva's punishment mirrors that of his counterpart, he could miss Everton's next two Premier League fixtures against Chelsea at Goodison Park and against West Ham at the London Stadium.