Zurich claim Yapi-Yapo, 32, was left with torn anterior and interior cruciate ligaments, serious cartilage damage, a meniscus tear, a torn kneecap and deep bruising in his thigh after Wieser's challenge in their Swiss Super League fixture on Sunday.
Wieser was sent off for the challenge, which saw his boot slam into the right knee of Yapi-Yapo in Zurich's 1-0 win.
Zurich president Ancillo Canepa said further action will be pursued by the club.
"His knees, just about everything is broken which can be broken. I cannot accept something so simple. This will have consequences," Canepa told Blick.ch.
Aarau published an apology from Liechtenstein international Wieser on their club website on Monday.
"I want to apologise in due form at Gilles Yapi and FC Zurich for the committed foul. It was never my intention to hurt Gilles," a translation of Wieser's statement read.
"It is difficult to explain in retrospect, what happened on the field within a fraction of a second. As a young player I was missing the experience in this situation to correctly assess the situation and I lack the words to explain everything in detail.
"Was it a reflex? An incorrect assessment? I do not want my explanations to sound like an excuse, I can only repeat that it is not my intention to injure my opponent when challenging for the ball.
"I live for football and have never been regarded as a bully and will stand in the future for fairness in my profession. I am heartbroken that Gilles will not be able to play football for a long time after this collision.
"I have visited Gilles still in the dressing room and apologised to him personally and would like to send to take this opportunity once again best wishes to Zurich.
"I hope that we continue to meet with respect off the pitch, and athletic competition on the field is soon possible."
