The first blast occurred around 2.00am (2100 GMT) in an upmarket shopping area close to the city centre.
“One watchman has died in the hospital; he was very critically wounded and did not survive. The second watchman is getting medical treatment,” said Chaudhry Hafiz Hussain, a senior police official.
He said it was not clear if the blast was the result of a suicide bomb. There was no immediate claim of responsibility but the blasts came after three days of air strikes by the Pakistani military against militant hideouts that have killed at least 75 people.
Local television footage of the first blast showed broken glass and branches strewn across the pavement.
Mohammad Ali, another police official, told reporters that the second bomb went off in a car.
“The low-intensity explosive was planted in a car. The blast has badly damaged the car but no one was hurt,” he said.
The second blast came around half an hour after the first and was in a different part of the capital.
The attacks were the first in Islamabad since an explosion tore through a fruit and vegetable market in April, killing at least 22 people.
The latest blasts came after more than three months of stop-start peace talks between the government and the Tehreek-e-Taliban Pakistan (TTP), which have made little progress since they began in February.
A monthlong ceasefire between Pakistan and the Taliban, who have waged a seven-year insurgency, expired last month.