Antares, built by Orbital Sciences Corp, combusted seconds after leaving the seaside launch pad at Wallops Flight Facility.
The cause of the cargo ship malfunction has yet to be determined.
The initial planned launch of the spacecraft on Monday was delayed due to a yacht in the surrounding danger zone.
The flight was expected to be the third contracted mission with the National Aeronautics and Space Administration.
The rocket was due to carry nearly 5,000lb (2,200kgs) of supplies to six astronauts aboard the International Space Station (ISS).
It included equipment for astronauts to conduct tests on blood flow to the human brain and to analyse meteors.
There was also equipment for experiments to examine the growth of pea shoots in orbit and how the body's immune system reacts to space travel.
More than 1,300lb (600kg) of food was on board, including pre-packaged meals and freeze-dried crab cakes.
"We will understand what happened, hopefully soon, and we'll get things back on track," said Frank Culbertson, executive vice-president of Orbital Sciences.
"We've all seen this happen in our business before, and we've all seen the teams recover from this, and we will do the same."
No-one was injured, said Mr Culbertson, and an investigation team was going through the data to try to establish the cause.
He added it was possible his company's staff had triggered the rocket's destruct mechanism after the launch went wrong, but that he was not certain.
The examination of debris around the site would begin on Wednesday morning, Mr Culbertson said.
But he urged locals to avoid the crash area as the rocket had been carrying "hazardous materials".
"Certainly don't go souvenir hunting along the beach," he said.
+ 5,000 kg
payload capacity
First flew:  2013
Stages:  2
Height*: 41.9 m
First-stage thrust:  734,000 lbs
Russia's space agency conducted its own launch to the ISS on Wednesday.
The operation, which by chance was on the same day as the Antares launch, was planned long before Wednesday's accident, officials said.
Investigators will not jump to conclusions but one line of inquiry will surely focus on the AJ-26 engines used to lift the rocket away from the pad, says BBC science correspondent Jonathan Amos.
"These are actually modified Russian-built power units that were originally developed for the ill-fated Soviet Moon rocket, the N-1.
"They have been refurbished to modern standards, but one blew up in ground testing earlier this year."
This new rocket was part of Nasa's effort to contract out "routine" cargo resupply to the International Space Station. But if we needed reminding that nothing in space is routine then this explosion has brought that message home in spectacular fashion.
The US space agency "seeded" development of Antares - and the supply ship it launches, Cygnus - by giving incentive payments to manufacturer Orbital Sciences Corporation, to help them develop a low-cost, commercial follow-on to fill the cargo gap left by the retired space shuttles.
The blast is likely to have seriously damaged the launch pad and support infrastructure, meaning that even if the fault is quickly identified and corrected, restarting Antares flights again may take a long time.
However, there should be no immediate threat to supplies for astronauts on the space station. The Cygnus cargo ship that was on top of the Antares is one of a fleet of vehicles that are used in this role. These other robotic vessels, launched atop other rockets, will now have to pick up the slack.
There is no doubting the explosion is a major setback for Orbital Sciences Corporation, and its plans to market Antares as a multi-purpose, commercial launcher. Confidence always takes a hit in the wake of a failure. But Orbital has the expertise to come back - as it has done after previous launch failures.
An unmanned supply rocket bound for the International Space Station has exploded shortly after its launch from the US state of Virginia.