The Los Angeles Times reported that state-owned Fidelity Printers & Refiners was thrown into crisis earlier this month by a lack of paper, following the German paper merchant's refusal to supply it.
The US newspaper said printing at Fidelity has slowed down and that two-thirds of the 1,000 staff have left.
One senior member of staff at the company said paper would run out in Zimbabwe within two weeks.
Fidelity is understood to print the money paid to police, soldiers and intelligence agents in Zimbabwe.
Last year hyperinflation meant it was printing $1m notes, and this year the company has had to print $500m and even $50bn notes.
Zimbabwe 'running out of paper to print money on'
Zimbabwe "could run out of paper to print money on", following a supplier's decision to end paper supply to the country.
