Kudus has made 19 Premier League appearances for Spurs this season, scoring twice and providing five assists. The 25-year-old Ghana international went down off the ball during the draw that left them 14th in the table.
"That is one where we expect him back after the March international break," Frank told reporters on Thursday.
The international break is scheduled from March 23rd to 31st.
"(Midfielder) Lucas Bergvall is being assessed today. Same with Rodrigo Bentancur. Rodri has a hamstring injury, looks like a bigger one, unfortunately. We don’t know the time frame," Frank said.
Spurs host Aston Villa in the FA Cup third round on Saturday.