The Barcelona superstar beat Paris Saint-Germain forward Neymar Jr, Edin Dzeko of AS Roma and Juventus forward Paulo Dybala to the award.
Messi retained the award which he won in the opening matchday of the competition after his hattrick over PSV Einhdoven.
The 31-year-old Argentine Maestro scored two goals against Tottenham unlike rivals Dzeko, Neymar and Dybala who scored three goals in their respective matches against Vitoria Plzen, Red Star Belgrade and Young Boys.
Messi's performance against Tottenham was so impressive that several media outlets hailed the Argentine superstar as one of the greatest of all time and was hailed by pundits .
The Barcelona captain will hope to recreate his heroics when he and his teammates joint group travel to face joint group leaders Inter Milan in their next Champions League outing after the international break.
Rakitic wins Goal of the Week
Barcelona midfielder Ivan Rakitic scooped the Goal of the Week award for matchday two of the UEFA Champions League.
The 31-year-old scored an incredible volley for Barcelona against Tottenham at Wembley as the Catalan giants cruised to a 4-2 victory.
Rakitic displaces Inter Milan forward Mauro Icardi who won the award for the last matchday also against Tottenham.
He beat Paris Saint-Germain, Dybala and Clubbe Brugge forward Arnaut Groeneveld Danjuma.