The Spurs striker has damaged ankle ligaments and could be sidelined for as many as eight weeks which will give Janssen, who joined from AZ Alkmaar for £17million, the chance to shine for Mauricio Pochettino.
The Spurs boss said: "It's true that it's a big opportunity for Janssen to show what he can do and he has to be ready now that Harry is injured.
"There is scope for him to play more from the start. Janssen is a good profile for us. He's a fighter, the mentality is fantastic and fits very well with us in the team. Only he needs time to adapt his game to the team.
"Now I think he will have a big opportunity to show his real quality. He has already shown the supporters he has a big passion to play. They have been excited to see him on the pitch and the energy he brings. Now he needs to be calm."
Janssen is expected led the attacking line when Spurs meet League One club Gillingham in the third round of the EFL Cup at White Hart Lane on Wednesday night.