But they will not lose any draft picks or premiership points.
The Power have accepted the penalty, again acknowledging their mistake.
Friday's sanction follows a league investigation into the Power's handling of Aliir Aliir after his head clash with teammate Lachie Jones during last Saturday night's Showdown against Adelaide.
Port Adelaide club doctor Mark Fisher conceded he should have put Aliir through the standardised 'SCAT5' concussion test after the head injury assessment.
Fisher's error - branded a "big mistake" by Power coach Ken Hinkley - has put the club under intense scrutiny.
"Our club understands the health and safety of players at all levels of the game is the key priority and we understand concussion and the protection of the brain health of all those playing our game is paramount," Port football boss Chris Davies said in a club statement.
"As we said publicly earlier in the week, we accept we made a significant mistake in not following the concussion guidelines appropriately. Our club doctor owned the mistake and publicly acknowledged his error.
"We accept the penalty handed down by the AFL and now look forward to cooperating with AFL chief medical officer Michael Makdissi to review the weekend's incident to ensure all our club medical officers are fully cognisant of the AFL's expectations regarding the concussion guidelines."
The Aliir controversy has come with head injuries now a massive issue in the game.
A number of former players are suing the league and their clubs, seeking compensation for the effects of concussion from their careers.
In a league statement on Friday, AFL general counsel Stephen Meade said Port Adelaide had understood the error and taken full responsibility for it.
"The AFL concussion protocols are some of the most stringent that exist in world sport, however, they require strict and consistent adherence to protect the health and safety of our players," Meade said.
"In this instance Port Adelaide admitted that Aliir should have undergone SCAT5 testing at the time immediately following the collision on Saturday night.
"By not undertaking the test, and Aliir returning to the game without being subject to that further detailed assessment, Aliir's wellbeing was potentially at increased risk.
"The health and safety of all players is paramount, and this will continue to be the focus for our clubs and for the AFL."
Makdissi will conduct a review of the Aliir incident before Port's away game against Geelong on Saturday night.
Half of the Power's fine will be included in their football department soft cap this season.
The balance will sit outside the cap unless a similar breach occurs before the end of the AFL and AFLW seasons next year.
Aliir and Jones will miss Saturday's visit to Geelong under the AFL's concussion protocols.
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