From MozillaZine Knowledge Base

Windows Update will not work in Mozilla Suite or Firefox because it uses IE-only scripts and ActiveX controls. Unless Microsoft makes some dramatic changes to their service it will not work with any other browser than Internet Explorer.

Alternate solutions

• Windows XP can be configured to automatically download any critical updates.
• The IE View extension can be configured to automatically open Windows Update in IE instead of Mozilla Suite or Firefox.
• IE Tab lets you embed Internet Explorer in Mozilla/Firefox tabs.
• WindizUpdate unofficially provides access to updates directly in Firefox, Opera, K-Meleon, Mozilla or Netscape. Does not use ActiveX. Works with any 32-bit windows flavors.