How to SELECT from SHOW TABLE STATUS results
This has more columns than SHOW TABLE STATUS; but does the trick:

SELECT * FROM information_schema.tables WHERE table_schema = DATABASE();


UPDATE 2011-06-07 19:02

SELECT table_name,Engine,Version,Row_format,table_rows,Avg_row_length,
Data_length,Max_data_length,Index_length,Data_free,Auto_increment,
Create_time,Update_time,Check_time,table_collation,Checksum,
Create_options,table_comment FROM information_schema.tables
WHERE table_schema = DATABASE();


These queries work if you set the current database.

You can also hard code the specific database:

SELECT table_name,Engine,Version,Row_format,table_rows,Avg_row_length,
Data_length,Max_data_length,Index_length,Data_free,Auto_increment,
Create_time,Update_time,Check_time,table_collation,Checksum,
Create_options,table_comment FROM information_schema.tables
WHERE table_schema = 'mysql';