According to Microsoft:
The Minesweeper game provided with
Microsoft Windows operating system
version 3.1 or in the Windows
Entertainment Pack version 1 cannot be
played without a mouse unless you
install the Trace Access Pack for
Windows. With the Trace Access Pack
installed you can use the numeric
keypad to move the mouse.
In later versions of Windows, you can use MouseKeys to use the numeric keypad to move the mouse.
However, a minesweeper wiki article indicates that versions of Minesweeper included with Vista or later operating systems have keyboard support:
In Vista or later it is easier to skip
MouseKeys and just use the keyboard.
Arrow keys move the cursor one square
at a time. Hit [Enter] to click, press
1 to flag and [Shift][Enter] to
chord. It is also possible to use
[Spacebar] to click, [Shift][Spacebar]
to flag or chord. In all versions [F2]
starts a new game and [Alt] allows you
to view the menus.