Workers were reportedly taken from a dormitory where they were staying on the outskirts of the town of Dumeir.
A factory administrator said no-one had been able to contact the workers since the assault on Monday.
The area around Dumeir has seen fierce fighting between government forces and IS in recent days.
The workers were employed at the Badiyah factory, just outside Dumeir, about 25 miles (40km) from the capital.
There are conflicting reports as to the number of those who are missing.
UK-based monitoring group the Syrian Observatory for Human Rights, said "dozens" of staff were believed to have been taken by IS to an unknown location.
The factory administrator put the number at 250, while rebel sources said it did not exceed 200.
A local resident told AFP news agency: "We haven't been able to reach our family members since noon on Monday after an attack by Daesh [IS] on the factory.
"We have no information about where they are," they added.
Efforts are under way to secure the workers' release, with indirect contacts said to have been made.
Earlier this week IS said it had launched several attacks around north-east Damascus, including Tishrin power station and Dumeir military airport.
A Syrian military source told Reuters there had been attacks but all of the militants who took part in them had been killed.
It comes almost two weeks after Syrian and allied forces recaptured the ancient city of Palmyra from IS, in what was seen as a significant loss to the militant group, which had held the city since last May.
Dozens of people are reported missing in the wake of an attack by the so-called Islamic State (IS) on a cement factory east of Damascus.