Early and effective prevention steps, including largely closing its borders, had succeeded in shielding Taiwan from the worst of the pandemic.
But cases have surged in recent weeks, prompting the government to limit personal gatherings and shut entertainment venues while it tries to speed up its vaccination programme.
The new money is in addition to previously announced stimulus spending worth T$420 billion, and the funding will run until June 30 of next year.
The central bank is also running a separate T$400 billion scheme to provide preferential loans to small and medium-sized business.
Taiwan's government has repeatedly sought to allay fears that the current outbreak of domestic infections will affect the export-dependent economy, a major global supplier of semiconductors.
Taiwan's central bank said on Monday it was paying close attention to how the spread of the virus could affect economic growth and that it will act if needed to ensure financial stability.
However, Taiwan's stock market has largely shaken off concerns about the coronavirus impact, with the benchmark index closing up 1.2% on Monday.
Infections have been heavily concentrated in Taipei and its nearby cities, and the numbers are beginning to fall.
($1 = 27.6240 Taiwan dollars)
(Reporting by Yimou Lee and Ben BlanchardEditing by Shri Navaratnam and Lincoln Feast.)