`Tools` > `Options` > `Query Results` > `SQL Server` > `Results to Text (or Grid if you want)` > `Include columns headers in the result set`
Uncheck the last option of `Include columns headers in the result set`

[Info from this question][1] - for further reading

[1]: http://%20%20%20%20https://stackoverflow.com/questions/10677133/saving-results-with-headers-in-sql-server-management-studio/10677148#10677148

`Tools` > `Options` > `Query Results` > `SQL Server` > `Results to Text (or Grid if you want)` > `Include columns headers in the result set`
You might need to close and reopen SSMS after changing this option.

**On the SQL Editor Toolbar you can select save to file without having to restart SSMS**