Herrera, who scored on his last outing in the 4-4 draw at Amiens on February 15, has a thigh muscle injury and is likely to be missing for between six and eight weeks.
It means both players will be unavailable for the visit of Dortmund to Parc des Princes on March 11, as PSG attempt to overturn a 2-1 deficit from the first leg.
They will sit out Saturday's Ligue 1 match at home to Dijon and the league trip to Strasbourg on March 7, as well as the Coupe de France semi-final away to Lyon on March 4.
Thiago Silva will hope to return for the meeting with Nice on March 15, while midfielder Herrera is unlikely to play again until April.
Thiago Silva, 35, has made 30 appearances in all competitions for Thomas Tuchel's side this season.
Herrera, who joined on a free transfer last year after his Manchester United contract expired, has played 18 times for the French champions.