Without having any details on the query or on the tables involved in the query, it is quite difficult to answer this question.
Most likely it is because of a lot of data in the table and a missing index on the field you are querying.
This would explain why it is slow on the production box, but fast on the dev box (since there's less data).
To answer the question better, could you provide us with more details? Table structure, query, number of rows in the table, etc. ?
More assumptions: Disk I/O on the app server could be a problem, maybe the log files in MySql are not properly configured (especially with InnoDB this could lead to a problem). Maybe there's a load-heavy query running too often? Table locks when multiple users write to/read from the same tables?
As I said, without having more details, it is quite difficult to guess. But I hope, at least I could point you in the right direction.