Nagatomo is recovering from a knee injury. CSKA Moscow said Honda is unfit, but has not elaborated on the specifics of his condition.
The 23-man squad named by Japan coach Alberto Zaccheroni on Thursday does include 13 Europe-based players including Manchester United's Shinji Kagawa and Stuttgart forward Shinji Okazaki, who scored twice against Latvia in a friendly last month.
"Everyone knows how highly I value (Honda and Nagatomo) but it's not the first time we have been without them," Zaccheroni said. "The players who have replaced them have always done a good job."
The squad will warm up for the Jordan match with a friendly against Canada at Doha on March 22. A win for Zaccheroni's side against Jordan should secure it a place at Brazil 2014.
A draw would also be enough to earn Japan one of the two automatic World Cup places from their group if Oman can hold Australia to a draw.
Forward Yuki Otsu of Dutch club VVV Venlo retains his place in the squad after making his debut as a substitute against Latvia.
Goalkeepers: Eiji Kawashima (Standard Liege), Shusaku Nishikawa (Sanfrecce Hiroshima), Shuichi Gonda (FC Tokyo)
Defenders: Yuichi Komano (Jubilo Iwata), Yasuyuki Konno (Gamba Osaka), Yuzo Kurihara (Yokohama F Marinos), Masahiko Inoha (Jubilo Iwata), Atsuto Uchida (Schalke), Maya Yoshida (Southampton), Hiroki Sakai (Hannover), Gotoku Sakai (Stuttgart)
Midfielders: Yasuhito Endo (Gamba Osaka), Kengo Nakamura (Kawasaki Frontale), Makoto Hasebe (Wolfsburg), Hajime Hosogai (Bayer Leverkusen), Hideto Takahashi (FC Tokyo)
Forwards: Ryoichi Maeda (Jubilo Iwata), Shinji Okazaki (Stuttgart), Mike Havenaar (Vitesse Arnhem), Takashi Inui (Eintracht Frankfurt), Shinji Kagawa (Manchester United), Hiroshi Kiyotake (Nuremberg), Yuki Otsu (VVV Venlo).