The group said it had made a strong start to 2020 in January but saw a significant slowdown in February after widespread storms hit Britain, while it also called out staff wages and pork commodities driving cost inflation.
The United Kingdom has had 39 confirmed cases of coronavirus, and Prime Minister Boris Johnson said on Monday that a "very significant expansion" was possible and the country should be prepared for it.
"The issue for us is what happens if it becomes more widespread across the nation - how that affects the way people move, the way people shop, the way people travel or not to work," Greggs chief executive Roger Whiteside told Reuters.
"In that sense you end up with demand impact," he said. "We're in uncharted territory."
The CEO said Greggs still expected to make progress in 2020 after a record 2019.
Shares in the firm were up 2.9% at 0940 GMT, extending gains over the last year to 20% and valuing the business at 2.19 billion pounds ($2.8 billion).
Greggs, which trades from over 2,050 outlets in the UK, said pretax profit excluding exceptional items rose 114.2 million pounds in the year to Dec. 28, ahead of analysts' expectations and up from 89.8 million pounds in 2018.
Total sales rose 13.5% to 1.17 billion pounds, helped by a net 97 new shop openings and the popularity of new products such as its vegan-friendly sausage roll.
Company-managed shop like-for-like sales rose 9.2% in 2019, but growth dipped to 7.5% in the nine weeks to Feb. 29 due to the storms.
One of the storms flooded a Greggs bakery just outside Cardiff which meant it was unable to supply 40 shops which had to close for a few days.
Greggs competes in a UK "food-to-go" market that is forecast to be worth 23.4 billion pounds by 2024, up from 18.5 billion pounds in 2019, growing by 26.4%, according to industry researcher IGD.
It sees opportunities for further growth by making its products more accessible and convenient for consumers.
In January it joined forces with online food ordering company Just Eat to offer home delivery across Britain, while in February it said it was partnering with supermarket group Asda to trial concessions in its stores. It is also experimenting with extended store opening times.
Greggs increased its total dividend by 25.8% to 44.9 pence and said it would consider payment of another special dividend at the time of its interim results.
By James Davey
