Born in the neighbourhood of
Mamilla in
West Jerusalem, Malmilian had a playing career in the
Liga Leumit at
Beitar Jerusalem. At an early age, he joined the youth system of Beitar. At the age of sixteen, Malmilian had his first appearance in the senior team of Beitar. In this first match he scored a stunning goal from a corner kick. Malmilian had his big breakthrough in the 1976 season. He led the squad to the second place of the league and won Beitar's first important trophy, the
Israeli Cup, after his goal in the 90th minute in the Final sealed the title. He was chosen as Player of the Season and was convoked to the National Team even before at the age of 18. This made Uri the youngest player ever to be convoked to
Israel national football team. In 1979 Malmilian received a lucrative offer from French club
Paris Saint-Germain but he decided to keep playing with Beitar. In the next few years he formed a devastating trio with team-mates
Danny Neuman and
Victor Levy. In 1986 Malmilian was the Top Scorer of the Israeli league with 14 goals in 30 matches, and in 1987, he coupled with
Eli Ohana to bring the club its first championship. In 1989, he won another Israeli Cup and then surprisingly announced a move to rival club
Maccabi Tel Aviv. With Maccabi, Malmilian won another championship in 1992. In 1993 Malmilian retired from active play. ==Managerial career==