"Temporary appointment. Not for long," Israel's Defence Minister Yoav Gallant posted on X with a photo of Qassem.
Earlier, Iran-backed Hezbollah said in a written statement that its Shura Council had elected Qassem, 71, in accordance with its established mechanism for choosing a secretary general.
Qassem was appointed as Hezbollah's deputy chief in 1991 by the armed group's then-secretary general Abbas al-Musawi, who was killed by an Israeli helicopter attack the following year.
Qassem remained in his role when Nasrallah became leader, and has long been one of Hezbollah's leading spokesmen, conducting interviews with foreign media, including while cross-border hostilities with Israel raged over the last year.
Nasrallah was killed on Sept. 27 in an Israeli air attack on Beirut's southern suburbs, known as Dahiyeh, and senior Hezbollah figure Hashem Safieddine - considered the most likely successor - was killed in Israeli strikes a week later.
Since Nasrallah's killing, Qassem has given three televised addresses, including one on Oct. 8 in which he said the armed group supported efforts to reach a ceasefire for Lebanon.
He is considered by many in Lebanon to lack the charisma and gravitas of Nasrallah.
In its official Arabic account on X, the Israeli government said: "His tenure in this position may be the shortest in the history of this terrorist organization if he follows in the footsteps of his predecessors Hassan Nasrallah and Hashem Safieddine."
"There is no solution in Lebanon except to dismantle this organization as a military force," it wrote.
