Town fans were offered the opportunity to park at the Conference South club for free ahead of Sunday's play-off final against Rotherham at Wembley.
But the club has been swamped with requests - and has now confirmed it is full.
Wealdstone club liaison officer James Klarfeld said: "I've been inundated with calls - working until 11pm to call people back.
"At one stage I turned my phone off for five minutes to have a break.
"Any money raised from catering will go back into the game - and fans have jumped at the chance rather than paying for parking.
"The response has been phenomenal and I'm sure everyone will have a great day with us."