Silva signed for Leicester in 2017 but has featured just 21 times for the Foxes in his spell at the King Power Stadium.
He spent the second half of last season on loan at Monaco and will return to the Stade Louis II for the remainder of the 2019-20 campaign.
The move sees Silva link up again with Islam Slimani, who joined Monaco in a temporary deal on Wednesday.
Silva helped Monaco remain in Ligue 1 last season and goes back to the club with Leonardo Jardim's men having endured an awful start to the season.
Monaco have suffered successive 3-0 defeats to Lyon and Metz, having a man sent off in each of those games.