The Saints have been drawn against the Lithuanian outfit in the Europa League first qualifying round, while Drogheda United face a trip to Sweden and Derry City take on Trabzonspor
The Saints, who currently lead the Airtricity Premier Division, will take on the Lithuanian outfit as they aim to reach the second qualifying round. St Pat's will be away in the first leg on July 4 before hosting Zalgiris on July 11 at Richmond Park in the second leg.
Runners-up in the 2012 Airtricity Premier Division Drogheda United will take on Swedish side Malmo FF. Meanwhile, Irish League side Crusaders have been drawn against Norwegian club Rosenborg for the second consecutive season. Glentoran will face Icelandic side KR, while Linfield take on Faroe Islands outfit IF Fuglafjordur.
FAI Cup winners Derry City will face Turkish team Trabzonspor in the second qualifying round, while the winner of Drogheda United's clash with Malmo will take on Scottish Premier League side Hibernian.
Should they progress to the second qualifying round, St Patrick's Athletic will face the winner of the tie between FK Teteks and Pyunik, while Irish League side Glentoran could face Belgian side Standard Liege if they can overcome KR.
Crusaders could come up against Scottish side St Johnstone if they can defeat Rosenborg in the first qualifying round, while Linfield will play Greek side Skodi Xanthi should they defeat IF Fuglafjordur.
All 38 first qualifying round ties are played on July 4 and 11 with the reward for the winners a place in the second qualifying round on July 18 and 25.