Media reports in Lebanon said buildings were on fire after the attacks by Israel.
A spokesperson for the Israeli government said the strikes were launched after a woman died and eight other people were injured in a rocket attack fired from Lebanon on the Safed area in northern Israel, in which a military base was also hit.
Hezbollah is thought to be behind the initial rocket attack, but has not claimed responsibility.
The armed group did not announce any operations on Wednesday – but the head of its executive council warned the Israeli attacks “cannot pass without a response”.
Latest exchange between Israel and Lebanon is unlikely to change status quo
In a statement, the Israel Defence Forces (IDF) said: “A short while ago, IDF fighter jets struck a series of Hezbollah terror targets in the areas of Jabal el Braij, Houneh, Dunin, Aadchit and Souaneh.
“Among the targets struck were military compounds, operational control rooms, and terror infrastructure used by Hezbollah terrorists.
Cross-border shelling has already killed more than 200 people in Lebanon, including more than 170 Hezbollah fighters, as well as around a dozen Israeli troops and some Israeli civilians.
Hezbollah and the Israeli military have been exchanging fire for more than four months.
It came after the armed group launched rockets across the disputed frontier in support of its Palestinian ally Hamas, which launched a deadly assault on Israel last October.
The exchange in fire has also displaced tens of thousands of people in the border areas of each country.