Drescher was joined by her costars, including Carly Rae Jepsen, to toast the occasion.
The new comedy, written by Robert Sternin and Prudence Fraser, stars Kerry Butler and Matt Walton.
The nanny from Flushing can now be seen in the musical through the end of June.
The husband-and-wife team shares thoughts on traveling from the hills of Hollywood to the dales of off-Broadway.
She'll take over the role of "Madame."