State television, citing its reporters on the scene, said the rocket hit near the entrance of the exhibition complex where the business fair opened this week.
The breaking news alert gave no details on the number of injured or the source of the rocket fire, and there was no immediate mention of the incident on state news agency SANA.
"We were preparing to receive visitors when I heard an explosion... then I saw smoke so the side of the of the entrance to the exhibition hall," said Iyad Jaber, 39, a Syrian working at a textile stand.
The Damascus International Fair was once the top event on Syria's economic calendar, but was last held in the summer of 2011, months after the start of a revolt against President Bashar al-Assad's government.
This year's fair opened on Thursday, and was scheduled to last 10 days.
Its general director, Fares al-Kartally, said the decision to hold the fair this year was a result of "the return of calm and stability in most regions" of Syria.
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"We want this fair to signal the start of (the country's) reconstruction," Kartally told AFP earlier this week.
While Damascus has been insulated from much of the worst violence of the country's war, several key rebel enclaves remain in the Eastern Ghouta region outside the city.
Fighters in the area have regularly fired rockets into the capital, and government warplanes have frequently carried out devastating raids across Eastern Ghouta.
But in recent weeks, much of the area has been quieter after the implementation in July of a "de-escalation zone" covering parts of Eastern Ghouta.
The United States and European countries, which have imposed sanctions on Assad's government, were not officially invited to participate in the fair, which was first held in 1954.
But a handful of European companies are participating on an individual basis in the event.
More than 330,000 people have been killed in Syria since the conflict began in March 2011 with anti-government protests.