Oakes will miss Falcons' European Challenge Cup tie against Kingston Park visitors Padova on Friday night, with Samoan international Rasmussen sitting out Worcester's tie against Viadana in the same competition on Saturday.
The players were reported by independent citing officers - Oakes for an alleged stamp on Wasps captain Lawrence Dallaglio during Falcons' 35-15 Guinness Premiership defeat last Sunday, while Rasmussen allegedly committed a dangerous tackle on Gloucester substitute Jonathan Pendlebury at Sixways two days earlier.
Oakes and Rasmussen will attend RFU hearings in London on Monday.
Referee Tony Spreadbury sin-binned Oakes, who joined Newcastle from Otley during the summer, but Rasmussen went unpunished by match official Dave Pearson.
"We have conducted our own disciplinary hearing," said Newcastle rugby director John Fletcher.
"And while we believe Jason's actions were careless rather than malicious, we still deem them worthy of a one-game suspension."
Oakes added: "I would like to express my remorse for the incident. I let myself and my team-mates down.
"I have an exemplary disciplinary record, and I look forward to resuming playing for the club following my suspension."