I borrow this thread because I have the same problem but with sqlite3.
checking for sqlite3.h... no
*** extconf.rb failed ***
Could not create Makefile due to some reason, probably lack of
necessary libraries and/or headers.
I tried to fix it by downloading the source code for sqlite from
http://www.sqlite.org/ and installing it. Now i have the sqlite3.h
header file and tried again with
gem install sqlite3-ruby --
The sqlite3.h file is in that directory but I get the same errors