Marquardt steps in to replace Chael Sonnen after Sonnen was indefinitely suspended by the UFC earlier this week.
The bout, which was first reported by ESPN, will have major implications on the respective futures of the two.
Akiyama is in desperate need of a win after suffering two straight losses in 2010, losing by triangle choke to Chris Leben at UFC 116 before dropping a unanimous decision to Michael Bisping at UFC 120.
At UFC 122, Marquardt came up on the short end of a No. 1 contenders fight in a decision loss to Yushin Okami.
Interestingly, the fight comes between two fighters who are both members of Team Greg Jackson, though Marquardt is a longtime member and Akiyama only spent time with the notable trainer prior to his last fight.
UFC 128 will emanate from the Prudential Center in Newark, New Jersey on March 19.