Several MPs, including all members of the liberal Meretz party, had threatened to boycott the ceremony, one of the president's most important and visible duties, if it was attended by Moshe Katsav.
The president's brother, Lior, said Katsav, who could soon be facing the most serious charges ever brought against an Israeli official, had decided to stay home to protect the dignity of the Knesset.
He told Army Radio: "There are apparently some members of Knesset who want to hover like vultures over carcasses and create provocations and to harm the image of the Knesset and symbols of power in Israel.
"The president will not be part of this charade."
Police on Sunday recommended that Katsav be indicted for rape, aggravated sexual assault and other counts, after completing a months-long investigation into complaints by women who worked for him.
"There are apparently some members of Knesset who want to hover like vultures over carcasses and create provocations and to harm the image of the Knesset and symbols of power in Israel"
Katsav denies any wrongdoing.
The final decision on whether to indict the president rests with Meni Mazuz, the attorney general.
Although a decision is likely to be weeks away, calls on Katsav to temporarily step aside or resign are growing.
Zion Amir, Katsav's lawyer, said his client has no plans to step down, though a formal indictment would "be a turning point that the president will have to take into consideration".
While Israel has a long history of political scandals, the charges that Katsav could face would be the most serious criminal counts ever brought against a serving official.
Katsav, who has not commented on the police recommendations, has said he is the victim of a conspiracy.
"We have no doubt of his innocence," Lior Katsav said.
"We know he is being framed and he is being blamed of things that did not happen."