"The criminal Kiev regime committed barbaric shelling of civilian objects - bridges on the administrative border between the Kherson Region and the Crimea near Chonhar," Saldo said on Telegram.
"The roadway on the bridges was damaged. There are no human casualties," Saldo said.
The official said that Kiev wants to intimidate residents of the Kherson Region and sow panic among the population, but they will not succeed. The traffic between the Kherson Region and the Crimea continues on reserve routes, Saldo added.
According to the preliminary assessment, the United Kingdom's Storm Shadow missiles were used in the attack.
Crimean head Sergey Aksenov said on Telegram that bomb disposal technicians were examining the sites of the Ukrainian strike on the Chonhar bridge. He confirmed that there were no casualties, adding that the information about the possibility of traffic across the bridge would be available within an hour.
Oleg Kryuchkov, Aksenov's adviser on information policy, said the shelling of the bridge would not be able to seriously disrupt the logistics of the land transport corridor between the Kherson Region and Crimea.
"Three checkpoints connect Crimea with the Kherson Region: two near Armiansk and one near Dzhankoi. The failure of one of them cannot drastically disrupt the transport logistics of the land transport corridor," he posted on Telegram.
Last week, Aksenov said that nine drones were detected over Crimea. Six of them were shot down and three were grounded by electronic warfare.
On Tuesday, Russian Defense Minister Sergei Shoigu said Ukraine was planning to strike Crimea and other territories with HIMARS and Storm Shadow cruise missiles.