No there isn’t. You need another command like echo -n, printf or tr. You could put a script somewhere in your PATH (eg. /usr/bin/) and make it executable with chmod +x /usr/bin/mydate
script:
#!/bin/sh
echo -n `date +"[%m-%d %H:%M:%S]"`
or use an alias.
alias mydate="echo -n `date +"[%m-%d %H:%M:%S]"`"