I had this problem in February while working on a Russian brochure. I found a support page that said Illustrator does not support Cyrillic fonts, however InDesign does, which is strange. I had to create text in InDesign, export as an EPS file for the client to open it in Illustrator. Here is what the web page says, and the link to it:
Support for Non-Roman Fonts in Illustrator
Adobe Illustrator 8.0 and later supports Roman fonts using the ISO Latin-1 character set, and in combination with a language kit or localized version of Windows or Mac OS, the Asiatic character sets of Chinese, Japanese, and Korean (CJK) double-byte fonts. Illustrator does not support the character sets of other non-Roman fonts (e.g., Arabic, Hebrew, or Cyrillic), even when you are using the appropriate language kit or localized version of the operating system.
Adobe Illustrator 7.0.x supports only Roman, CJK, and Cyrillic fonts.