@damienfrancois has the best answer. You can also use bash regex matching:
if [[ $string =~ ([^,]+).*"Interface "([^,]+) ]]; then
ip=${BASH_REMATCH[1]}
int=${BASH_REMATCH[2]}
fi
echo $ip; echo $int
192.168.1.1
GigabitEthernet1/0/13
With bash regexes, any literal text can be quoted (must be, if there's whitespace), but the regex metachars must not be quoted.