Table names appear in 'show tables'; but tables don't exist

[Jonathan Turkanis]

Hi,

Last night an application started reporting MySQL errors. I checked the logs and found errors of the form

ERROR 1146 (42S02): Table 'Database.Table' doesn't exist

When I run "show tables" I see the correct list of tables, but when I try to access any table, e.g. by running "SELECT * FROM Table" I get an error message saying that the table doesn't exist. When I run "repair table Table" I get

+----------------+--------+----------+--------------------------------------+
| Table | Op | Msg_type | Msg_text |
+----------------+--------+----------+--------------------------------------+
| Database.Table | repair | Error | Table 'Database.Table' doesn't exist |
| Database.Table | repair | error | Corrupt |
+----------------+--------+----------+--------------------------------------+

All the tables use the InnoDB storage engine.

What could cause this error, and is there any way to recover the data?