I have mistakenly written "Dear Sir" to a senior HR member, who is female, in an email. How should I professionally correct myself?

As a female senior HR professional, I'd add a bit of nuance to what Duncan wrote.

I live in the UAE, where there is a massive mix of nationalities. In many cases, if we haven't spoken on the phone already, I also wonder if the person I'm corresponding with is male or female.

If you've never had personal contact with that person, AND you did not write to them on a social network where you can see their picture, then writing "Dear Sir" is not really an issue so don't be too bothered about it - although I'd recommend that you change your "default" to Dear Sir/Madam in the future.

BUT, there is nothing I hate more than if someone contacts me on LinkedIn, where my photo is there and clearly shows I'm female, and writes to me "Dear Sir"... because it means the person does not pay attention and from there I assume he/she is just trying to send their message out to as many people as possible (a bit spammy), instead of writing something to me as a person ie writing something unique.

So if you did know the gender of the person because you met her or spoke to her on the phone, or wrote to her on LinkedIn where she shares her photo, a simple message like "Woops ! I just noticed that I addressed you as a Sir in my previous message. Force of habit... I'm sorry about that and did not mean to offend" should be enough.

It will show that you pay attention to detail and own up to your mistakes, which are 2 great qualities to display in the workplace. Personally, if I ever received this kind of message I would pay much more attention to the sender - in a positive way.

Be a gentlemen to send back a correction   e mail with your apology or pardon,

and be careful on it before send the email repeat it to your self one or two time. 

Nothing to worry about...Just be careful next time.

Apologies, and be careful for the next time not repetd.

Not a problem just write another email with your apology and be Careful next time.

write an apology and People these days are least bothered about the mails which begins with dear sir/madam the often ignore such mails so instead of mentioning sir /madam address them like Dear (office name) professionals ,

If you don't know the Hr Head in a person, that is not a problem.

But before you apply it is always good to know with whom you are meeting or to whom you are writing.

I think it's no problem on that

but you should be carful with top manager

send apology mail to her and mention Dear Mrs (Her name) ..

Send an apology email and be careful next time when to write an email, read carefully before sending. 

I would resend the email with the correct information apologising for the mistake and ask for the Senior Hr member to kindly disregard the wrong email

Well it depends on the communication pattern, if its repete communication and sender's profile is similar to receiver's then casual pattern can work well considering due respect in mind. If the communication is first time happening then protol needs to be followed Like "Dear Ms. ......."

An appology can work well but smartly practiced.