Do I have to guard against SQL injection if I used a dropdown?

Yes you need to protect against this.

Let me show you why, using Firefox's developer console:

If you don't cleanse this data, your database will be destroyed. (This might not be a totally valid SQL statement, but I hope I've gotten my point across.)

Just because you've limited what options are available in your dropdown does not mean you've limited the data I can send your server.

If you tried to restrict this further using behaviour on your page, my options include disabling that behaviour, or just writing a custom HTTP request to your server which imitates this form submission anyway. There's a tool called curl used for exactly that, and I think the command to submit this SQL injection anyway would look something like this:

curl --data "size=%27%29%3B%20DROP%20TABLE%20*%3B%20--"  http://www.example.com/profile/save

(This might not be a totally valid curl command, but again, I hope I've gotten my point across.)

So, I'll reiterate:

NEVER trust user input. ALWAYS protect yourself.

Don't assume any user input is ever safe. It's potentially unsafe even if it arrives through some means other than a form. None of it is ever trustworthy enough to forgo protecting yourself from SQL injection.

You could do something as simple as the following example to make sure the posted size is what you expect.

$possibleOptions = array('All', 'Large', 'Medium', 'Small');if(in_array($_POST['size'], $possibleOptions)) {    // Expected} else {    // Not Expected}

Then use mysqli_* if you are using a version of php >= 5.3.0 which you should be, to save your result. If used correctly this will help with sql injection.

As this question was tagged with sql-injection, here is an answer regarding this particular kind of attack:

As you've been told in the comments, you have to use prepared statements for the every single query involving any variable data, with no exceptions.

Regardless of any HTML stuff!
It is essential to understand that SQL queries have to be formatted properly regardless of any external factors, be it HTML input or anything else.

Although you can use white-listing suggested in other answers for the input validation purpose, it shouldn't affect any SQL-related actions - they have to remain the same, no matter if you validated HTML input or not. It means you still have to use prepared statements when adding any variables into the query.

Here you may find a thorough explanation, why prepared statements is a must and how to properly use them and where they aren't applicable and what to do in such case: The Hitchhiker's Guide to SQL Injection protection

Also, this question was tagged with mysqli. Mostly by accident, I presume, but anyway, I have to warn you that raw mysqli is not an adequate substitution for the old mysq_* functions. Simply because if used in the old style, it will add no security at all. While it's support for the prepared statements is painful and troublesome, to the point that average PHP user is just unable to endeavor them at all. Thus, if no ORM or some sort of abstraction library is option, then PDO is your only choice.