The blast hit the Green Trend party office of Saleh. He was evacuated and moved to a safe location. Later, photographs shared by a government official showed Saleh sitting in a garden with bloodstains on his right arm.
The attack occurred at around 4.40 pm on Sunday, and started with Asuicide car bombing followed by firing by four attackers, Ministry of Interior's spokesman Nusrat Rahimi said.
The attackers targeted the office of the political movement run by the former intelligence chief.
Rahimi said that while the gun battle was still ongoing, the first and second floors of the building had been cleared by security forces.
At least 40 people who were stuck inside the building during the attack were rescued.
While two of the gunmen were killed in the shootout, two attackers were still inside.
Wahidullah Mayar, a spokesman for Ministry of Public Health, said that at least two people were killed and 25 others were wounded in the attack on Green Trend office in Kabul.
President Ashraf Ghani said in a tweet: "My brother, true son of the Afghan soil and first VP candidate of my electoral team, Amrullah Saleh has survived a complex attack by enemies of the state. We are relieved and thank the almighty that the attack has failed."
The blast was large enough to be heard throughout the capital.
No group immediately claimed responsibility for the attack.
Condemning the attack, India said it stands in solidarity with the Government and the people of Afghanistan in their efforts to achieve enduring peace, security and stability in Afghanistan.
"This dastardly attack was also aimed at undermining the constitutional and democratic processes and institutions in Afghanistan," India said.
Sunday was the first day of campaigning for the presidential elections being held in September.
( With inputs from IANS )