Two hours after Kalam arrived at a high-security army airport in Srinagar on Wednesday, rebels threw the grenade at a security patrol, but missed their target.
Police said most of those injured in the attack at Anantag, 50km south of Srinagar, were civilians. Two victims were in critical condition.
"The blast caused chaos in the area, we've sealed it off," a police official said. Earlier, two separatists were killed in northern Baramulla district in a pre-dawn skirmish with security forces.
Kalam was whisked by helicopter from the army airport to visit troops in Kargil, high in the Himalayan heights.
Tight security surrounded his visit to the soldiers stationed in Kargil that was the scene of a bloody two-month confrontation between Indian and Pakistani troops in 1999.
The one-day visit by Kalam, a Muslim, will be his second in two years and comes less than a month after Prime Minister Manmohan Singh visited the region, saying he wished to "put an end to this chapter of violence in Kashmir".
Decades old dispute
Kashmir is at the heart of nearly six decades of hostility between India and Pakistan. Each hold part of the territory, but claim it in full and have fought two wars over it.
India and Pakistan are engaged in a tentative peace process launched by former Indian prime minister Atal Behari Vajpayee in 2003, a year after the two countries nearly came to war again over Kashmir.
The 15-year-old revolt has claimed more than 40,000 lives since 1989 by official counts. Separatists say the toll is at least double.
India accuses Pakistan of fomenting the insurgency in Kashmir. Pakistan says it only gives moral and diplomatic support to a "freedom struggle".
Violence continues in Kashmir even though the New Delhi government says there has been a 60% drop in separatist incursions into Indian Kashmir from the Pakistani zone.