Ramos was substituted at half-time in Madrid's surprise 1-0 La Liga defeat to newly-promoted Cadiz on Saturday.
The centre-back suffered a knock to his left knee and was pictured sat in the stands with the knee wrapped in bags of ice during the second half.
Tests carried out on Sunday revealed that the Madrid and Spain captain had suffered no serious damage, sources told ESPN, and both the player and the club's medical team were happy with his progress on Monday morning.
Ramos will be fit for Saturday's game with Barca at Camp Nou, but is a doubt to start Madrid's opening Champions League Group B match against Shakhtar Donetsk at the Alfredo di Stefano stadium on Wednesday.
Odegaard, meanwhile, will miss a minimum of two to three weeks with a calf muscle problem picked up on international duty with Norway.
The 21-year-old playmaker featured in three games during the international break, starting in his country's Euro 2020 qualifying defeat to Serbia as well as UEFA Nations League wins over Romania and Northern Ireland.
Real Madrid confirmed Odegaard's calf injury on Friday, and sources have told ESPN he will now be absent for a busy period of fixtures that includes league matches against Barcelona, Huesca and Valencia and Champions League games with Borussia Monchengladbach and Inter Milan.
Madrid's loss to Cadiz on Saturday left them third in the La Liga table after picking up 10 points from five games, three points ahead of rivals Barcelona, who were also beaten by Getafe.