Insua has gradually moved ahead of Andrea Dossena, the £7 million summer signing, in the left back pecking order and has been hugely impressive in recent games which has saw the reds performances dramatically improve.
The player will be away until February 8th, missing vital clashes against Everton and Chelsea.
With Fabio Aurelio only just recovering and Arbeloa and Degan still out injured, the reds are looking very thin on the ground in terms of full backs.
Reds reserve defender Ronald Huth has also travelled to the tournament to represent Paraguay. It all kicks off on the 19th January.
Both players will leave before the end of this week.
Anfield Online wishes both players a succesful and injury free tournament.