The 28-year-old attracted summer interest from two Russian clubs and a Coca-Cola Championship outfit and has netted seven goals this season despite often finding himself on the bench.
Hearts chief Anatoliy Korobochka said: "Andrius has an ability to score goals from all areas in and around the box.
"He has adapted well to the physical style of football in Scotland and he clearly relishes the opportunity to play for Hearts - you can see that every time he scores.
"We do expect interest in Andrius in the transfer window as he is an excellent player, but he is very focused and dedicated to helping Hearts win silverware.
"While his scoring ratio is excellent, he is gaining a reputation as a player who scores in the big games but we know he is also capable of scoring against any team in the league or cup."