The two footballing giants have won the top European competition 11 times between them but, in a group with Barcelona, both desperately need three points.
Milan has tasted success in Europe's premier club competition on seven occasions - second only to Real Madrid - while Ajax has won the tournament four times.
But when it comes to recent form, Ajax certainly has the edge ahead of the fixture at the Amsterdam ArenA having thrashed Go Ahead Eagles 6-0 in its last outing.
On the other hand, Milan has struggled at the start of the new season, with Saturday's narrow 1-0 win over Sampdoria representing just the club's second in Serie A so far in 2013-14.
The Italians will at least be buoyed by the knowledge that they have already beaten Dutch opposition in the Champions League this term, with their group-stage participation sealed by a playoff round victory against PSV.
Massimiliano Allegri's team followed up that success with a 2-0 win against Celtic on matchday one, while Ajax found itself on the wrong end of a 4-0 humbling away to Barcelona.
Milan's hopes of taking a good result from the Amsterdam ArenA are likely to rest on the shoulders of four-goal forward Mario Balotelli, while Ajax will rely on Kolbeinn Sigthorsson - who has six goals in 10 appearances this term - to put chances away.
The two teams have plenty of history in Europe, having met in the finals of both the 1968-69 and 1994-95 editions of the competition.
Milan ran out a 4-1 winner in the former, with forward Pierino Prati notching a hat trick, while a solitary strike from Patrick Kluivert saw Ajax exact revenge 26 years later.
The last meetings between the clubs came in the group stages of the 2010-11 tournament, with Ajax taking a 2-0 win in Milan and the teams sharing a 1-1 draw in Amsterdam.
With Barcelona looking like a strong favorite to win Group H already, Ajax and Milan will hope to land an early blow in what could be a race for the second qualification spot.
The home side must bid for that win without the services of Thulani Serero (stomach) and Joel Veltman (knee) due to injury, though the Italians have a spate of problems in that regard.
Kaka, Mattia de Sciglio, Matias Silvestre and Giampaolo Pazzini (all knee) will miss out for Milan, though Stephan El Shaarawy, Riccardo Montolivo (both thigh) and Daniele Bonera (knee) could return.