How to change ibdata1 path in mysql?
I've just done what you want! You'll have to move the entire datadir and not just a single file - not sure if that's possible.

For example, in my datadir, you will find:

pol@pol:~/Downloads/sware/mysql/mysql-5.5.58-linux-glibc2.12-x86_64/data$ ls -lista
total 28724
32774484  5120 -rw-rw----  1 pol pol   5242880 Oct 24 12:47 ib_logfile0
32774483 18432 -rw-rw----  1 pol pol  18874368 Oct 24 12:47 ibdata1
32774487    16 -rw-rw----  1 pol pol     13498 Oct 24 12:47 mysql-bin.000001
32774488     4 drwx------  2 pol pol      4096 Oct 24 12:47 ptest
32774151     4 drwxrwxr-x  6 pol pol      4096 Oct 21 11:55 .
32774465     4 -rw-r-----  1 pol pol      2219 Oct 21 11:46 pol.err
32774486     4 -rw-rw----  1 pol pol         6 Oct 21 11:46 pol.pid
32774482     4 -rw-rw----  1 pol pol        19 Oct 21 11:46 mysql-bin.index
32774485  5120 -rw-rw----  1 pol pol   5242880 Oct 21 11:46 ib_logfile1
32643837     4 drwxrwxr-x 13 pol pol      4096 Oct 21 11:40 ..
32774334     4 drwx------  2 pol root     4096 Oct 21 11:34 mysql
32774404     4 drwx------  2 pol pol      4096 Oct 21 11:34 performance_schema
32774152     4 drwxrwxr-x  2 pol pol      4096 Oct 21 11:26 test


Files like ibdata1 and ib_logfile are very important! So, it's important to copy the whole datadir!

Step 0 - backup everything - DBA's motto - "Backup or F***up!" :-)

Also, you say that this is a production server - test on a non-prod
machine first.

First, take a copy of your datadir - mine's called simply data. As a dba, you should always have a path for backing out your changes!

cp -r ./data ./databak


Then copy your old data to your new directory - with your mysqld server stopped, otherwise you will have inconsistencies.

cp -r data datatest


Then remove your old data directory

rm -rf data


Edit your my.cnf file replacing your old datadir location with your new one, or adding it, if you were using a default.

vi my.cnf


Then kick off your server again.

Et voilà!