British media reported last week that tickets for the final were being resold on the website StubHub for more than £3,000 ($5,500) each, roughly six times the face value of the most expensive category on sale.
"The club has this week issued indefinite bans to three season ticket holders who have listed their UEFA Champions League final tickets for sale on a secondary ticketing platform," Tottenham said in a statement.
"Transferring or selling tickets on unofficially breaches our terms and conditions and is against the law.
The north London club also urged its supporters not to "ruin" the occasion of reaching their first ever Champions League final by trying to profit off fellow fans and said more bans could follow.
"We shall look to take the strongest possible action against anyone found to be engaging in such activity - including indefinite season ticket bans," Tottenham said.
Spurs are trying to cancel all tickets that have been sold on by supporters and said anyone carrying a resold ticket would be denied entry to the stadium.
Apart from the 34,000 tickets allocated to the two English clubs, 4,000 tickets were put on sale for fans worldwide on the UEFA website.
The remaining tickets were allocated to the local organising committee, UEFA, national associations, commercial partners and broadcasters.
