Can SHOW TABLE STATUS query performance on MySQL be improved ? - Amazon RDS
You may want to disable the variable innodb_stats_on_metadata.

According to the MySQL Documentation on innodb_stats_on_metadata


  When this variable is enabled (which is the default, as before the
  variable was created), InnoDB updates statistics during metadata
  statements such as SHOW TABLE STATUS or SHOW INDEX, or when accessing
  the INFORMATION_SCHEMA tables TABLES or STATISTICS. (These updates are
  similar to what happens for ANALYZE TABLE.) When disabled, InnoDB does
  not update statistics during these operations. Disabling this variable
  can improve access speed for schemas that have a large number of
  tables or indexes. It can also improve the stability of execution
  plans for queries that involve InnoDB tables.


Since you are using Amazon RDS, ask your DB Administrators to disable it. If your DBs are in a Shared Resource, my condolences...

UPDATE 2012-07-25 14:45 EDT

If you can download the RDS CLI, you can adjust innodb_stats_on_metadata in a customized DB Parameter Group. You will have to do the following:


mysqldump data out of RDS Server
destroy DB Server Instance
create DB Server Instance using your custom DB Parameter Group adjusted for innodb_stats_on_metadata
reimport the mysqldump into new DB Instance


Since Amazon RDS does not give away SUPER privilege, that's the only way to change a GLOBAL static option.

UPDATE 2012-07-27 16:34 EDT

Without SUPER Privilege, you can modify a DB Parameter Group for a given MySQL RDS Instance, and launch a reboot with one of the following:


rds-reboot-db-instance &lt;DBInstanceName&gt;
Click Reboot Button in the RDS Management Console