By combining egrep (called with the -l option so that positive matches return only filenames) with xargs you can perform arbitrary commands based on text matches:
[gnubeard@mothership: ~/mver]$ ls
destination example.fna non_example.fna
[gnubeard@mothership: ~/mver]$ cat example.fna
>>>>>>>>>
[gnubeard@mothership: ~/mver]$ cat non_example.fna
<<<<<<<<<
>>
[gnubeard@mothership: ~/mver]$ egrep -l '>{9}' *.fna | xargs -I{} mv {} destination/
[gnubeard@mothership: ~/mver]$ ls
destination non_example.fna
[gnubeard@mothership: ~/mver]$ ls destination/
example.fna
Edit: This doesn't match files with a certain number of instances of a character, if they're separated by other characters or newlines. I've created this short script that should operate as desired.
#! /usr/bin/env bash
DESTINATION=./destination
MATCH_CHAR='>'
MATCH_COUNT=9
for FILE in $1; do
MATCHES=$(grep -o $MATCH_CHAR $FILE | wc -l)
if [ $MATCHES -eq $MATCH_COUNT ]; then
mv $FILE $DESTINATION
fi
done
Example:
[gnubeard@mothership: ~/mver]$ ls
destination example.fna mver non_example.fna
[gnubeard@mothership: ~/mver]$ cat example.fna
>>
>>foo>>bar>>>baz
[gnubeard@mothership: ~/mver]$ cat non_example.fna
<<<<<<<<<
>>
[gnubeard@mothership: ~/mver]$ ./mver *.fna
[gnubeard@mothership: ~/mver]$ ls destination/
example.fna
[gnubeard@mothership: ~/mver]$ ls
destination mver non_example.fna