Vertonghen required extensive treatment after colliding with the back of fellow Belgium defender and Spurs team-mate Toby Alderweireld's head in the first half of Tuesday's 1-0 loss to his former club in London.
Despite initially being cleared to return to action, Vertonghen had to be withdrawn moments later and he needed to be helped from the pitch in worrying scenes, with brain injury charity Headway saying that the incident showed the need for "temporary concussion substitutions".
Spurs defended their handling of the incident and insisted they followed the correct guidelines, while manager Mauricio Pochettino praised the work of the club's medical staff.
Despite not sustaining a concussion, Vertonghen has been advised to undertake a "brief period of rehabilitation" before returning to training, making him a serious doubt to face Bournemouth on Saturday and also putting his participation in the crucial second leg at Johan Cruijff ArenA in question.
In an update on Vertonghen's condition posted on their website, the club said: "Following a thorough review over the past 48 hours by our medical staff as well as by an independent neurologist with special interest in sport-related concussion today, it has been concluded that Jan Vertonghen did not suffer a concussion during Tuesday's Champions League semi-final first leg against Ajax.
"The Belgium defender suffered an injury to his nose due to a challenge during the game which resulted in heavy bleeding. He was deemed fit to continue playing after an on-field assessment. All Football Association concussion guidelines were followed.
"Jan was immediately withdrawn as a result of the player informing medical staff that symptoms were developing suddenly and that he no longer felt stable standing up. We have been advised that this was the result of a presyncopal episode, a near faint.
"The specialist has recommended that the player undertakes a brief period of rehabilitation before returning to training."
In addition to their hopes of overturning their 1-0 deficit in Amsterdam, Spurs still have to contend with the final two games of the Premier League season as they seek to secure a top-four place.
Currently third in the table on 70 points, two ahead of Chelsea in fourth and four ahead of Arsenal in fifth, and can sure their place in next year's Champions League with a victory against Bournemouth.
Spurs will close out their season May 12 at home against Everton.