You should be able to do this by changing your ssh configuration from the default log-level of "info" to "error" (the next level up).
Refer to the ssh_config manual page:
LogLevel
Gives the verbosity level that is used when logging messages from ssh(1). The possible values are: QUIET, FATAL, ERROR, INFO, VERBOSE, DEBUG, DEBUG1, DEBUG2, and DEBUG3. The default is INFO. DEBUG and DEBUG1 are equivalent. DEBUG2 and DEBUG3 each specify higher levels of verbose output.
The source code for ssh tells the story:
/*
* Initialize "log" output. Since we are the client all output
* actually goes to stderr.
*/
log_init(av[0], options.log_level == -1 ? SYSLOG_LEVEL_INFO : options.log_level,
SYSLOG_FACILITY_USER, 1);
along with the definition of log_init:
void
log_init(char *av0, LogLevel level, SyslogFacility facility, int on_stderr)
{
i.e., all of the "log" messages go to the standard error, and you can only adjust how many you get. The one you do not want happens to be at the INFO level.