There’re many ways to accomplish this request. Here is a quite simple one which could be performed in Linux.

Prerequisite(s): mdbtools installed (get it at: http://mdbtools.sourceforge.net/)

#1. Export tables list under CSV format
mdb-export database.mdb table_name

#2. Convert mdb into a format required by MySQL
mdb-schema database.mdb | mysql -u username -p database_name

#3. Import table content
mdb-export -I database.mdb table_name | sed -e 's/)$/)\;/' | mysql -u username -p database_name

Probably this needs to have some more improvements, later.