Unknown assailants set on fire the anti-Morsi Rebel Campaign headquarters in Cairo's downtown district in the early hours of Friday, Al Ahram Arabic news website reports.
Assailants threw Molotov cocktails at the office, the group posted on its official Facebook page immediately after the attack.
The Rebel Campaign aims to force early presidential elections by gathering 15 million anti-Morsi signatures to outnumber the 13.2 votes that got him into office in June 2012.
Supporters of President Morsi charge that the Rebel campaign is anti-democratic as it attempts to prevent the elected president from finishing his 4-year term.
Campaign organisers expected only limited damages to the petition forms since members and volunteers managed to put out the fire.
Police arrived at the scene shortly after.
Campaign Spokesman Hassan Shahin sustained burns to his arm as he attempted to contain the fire, the group said.
Organisers said the group has received threats of physical harm from Islamist presidential supporters in recent days.
Shortly after the attack started, the group urged on its Facebook account for its campaigners and volunteers to rescue the office, where hundreds of thousands of petition forms are stored.
"Their attempts to intimidate rebels will only strengthen their determination to bring down the regime and press on with the revolution," Shahin declared early on Friday.
Rebel campaigners have been subject to a series of intimidation attacks, physical assaults and brief arrests and abductions throughout the past two weeks.
In a similar incident, the Free Egyptians Party headquarters in Cairo's Al-Zaher district was attacked, allegedly by President Morsi allies on Sunday and a number petition forms there were stolen.