Altman joined the youth squad of Maccabi Tel Aviv at the age of 11 and ever since showed remarkable performances for the team. In result for his good performances with the club, at the age of 17, he was signed by Fulham on a youth loan. After 24 appearances with the reserves team he signed a two-year professional contract with the club. On 27 June 2013, Altman was loaned back to Maccabi Tel Aviv. On 17 July 2013, Altman made his first ever official appearance with the senior team of Maccabi in an important match against Győri ETO FC in the 2013–14 UEFA Champions League qualifying rounds. On 20 October 2013, he made his league debut in a 1-0 victory against Ironi Ramat Hasharon. On 19 June 2015 signed with Hapoel Tel Aviv for 5 years.
On 28 June 2017 Altman signed a three-year contract with Panathinaikos from Hapoel Tel Aviv for a transfer fee of approximately €150,000. On 17 September 2017, he scored with a header the only goal in a 1-0 home win against Apollon Smyrni. The Israeli youth international was brought to the club as a virtual unknown from Hapoel Tel Aviv for a fee in the region of €150,000. This highlights the severe financial constraints impacting Marinos Ouzounidis. The attacking midfielder, however, has done relatively well barring an injury that kept him out for some time. His two goals in the first half of the season came in a home win against Apollon Smyrni and in a draw away against Xanthi. On 4 March 2018, Panathinaikos' Israeli attacking midfielder, Omri Altman, suffered cruciate ligament injury during away derby clash against Olympiacos and will miss the last six championship matches of the Greens and therefore the remainder of 2017-18 season. His return was initially pencilled in for September or October 2018, but it got delayed as he returned to his native Israel for further treatment. There had now been a new delay as Panathinaikos coach Giorgos Donis wants the midfielder to undergo a slow recovery process to ensure he is 100% fit before even being considered for the first team. The new return date is estimated to be January 2019, with heavier training commencing in December, that would make it 10 months on the sidelines for the 24 year old. On 21 January 2019, after a very difficult period for the midfielder marred by injury he returned to the squad in a 1-0 away loss against Lamia. On 16 February 2019, a month after his return he scored after a great pass from captain Dimitris Kourbelis and the Isralian chested the ball down superbly before firing a powerful shot beyond Nikos Papadopoulos from the edge of the penalty area, sealing a vital 1-0 home win game against Asteras Tripoli.
Return to Hapoel
On 14 July 2019 Altman returned to Hapoel Tel Aviv.
