The claims came three days after Egypt said that a "cell" of 49 men with links to Hezbollah had been arrested on suspicion of planning attacks aimed at destabilising the country and providing aid to Hamas, the Palestinian group controlling the Gaza strip.
The 25 men in custody were from places including Lebanon, Palestine, Egypt and Sudan, Shihab said.
Hassan Nasrallah, the secretary-general of Hezbollah, said on Friday that a member of its ranks who was sent to Egypt to provide help to Hamas had been arrested in November on charges of smuggling arms and equipment to Gaza via the strip's Egyptian border.
But he denied that Hezbollah was planning attacks against targets in Egypt.
Cairo's claims highlight the differences between Washington's allies in the region – Egypt, Israel and Saudi Arabia, and Iranian-backed groups such as Hezbollah and Palestinian Hamas.
Relations between Egypt and Hezbollah have worsened since Israel launched its 22-day war on Gaza with the stated aim of preventing rocket attacks from the Hamas-run coastal territory.
Nasrallah had accused Egypt of aiding Israel in its assault on Gaza by failing to open its border to allow Palestinians to leave the besieged territory.
More than 1,300 Palestinians, at least half of them civilians, were killed during the conflict before Hamas and Israel each issued unilateral ceasefire orders.