According to media reports, former Greece international Dabizas, 40, was physically and verbally attacked by four Panathinaikos fans outside the team's Apostolos Nikolaidis stadium on Sunday morning after watching the under-20 team.
"Panathinaikos condemns the behaviour of the individuals involved in the attack against the team's technical director Nikos Dabizas," the club said in a statement.
"Nikos is a capable, worthy and hard-working member of the club and is doing his best for the good of a Panathinaikos team which is struggling to be reborn ... in a hostile environment."
The club added that the former Newcastle United defender did not want to press charges against his attackers.
Dabizas, who ended his playing career at AEL Larissa in 2001, recently joined the club to oversee player transfers after they failed to qualify for Europe for the first time since 1997.
Panathinaikos beat Panaitolikos in their opening game of the season but last weekend's 3-0 defeat by Panionios and Saturday's disappointing home draw against Veria sparked heavy criticism of Yannis Anastasiou's team.
- Sports & Recreation
- Nikos Dabizas