Smith is expected to make his debut at the weekend against Nottingham Forest.
"Adam is a player I have been following for some time," said Lions boss Kenny Jackett.
"He's a very promising young full-back and with both Jack and Alan unavailable for Saturday this was an opportunity to bring Adam in to fill that gap in the short-term and hopefully for him to get more first team experience over the next couple of months with us."
The England Under-21 international has made two first-team appearances for Spurs and had loan spells at Wycombe, Torquay, Bournemouth and MK Dons.
Source: team_talk
