SHOW TABLE STATUS very slow on InnoDB
Here is a quick-and-dirty solution:

set global innodb_stats_on_metadata = 0;
show table status;
set global innodb_stats_on_metadata = 1;


You want to turn innodb_stats_on_metadata  on immediately after the show table status; so that metadata is used efficiently for Query Optimizer analysis when evaluating queries involving InnoDB. Leaving it off will provide more stable Query Execution plans, but the index statistics grow stale quickly in a heavy-write environment.

Give it a Try !!!