Yes that will not hurt the tree. You might lose a little fruit next year that may have formed on thos branches but I suspect not enough to make a difference.

Just follow good pruning practices as outlined by the U of Fl and go for it . Try this site : http://edis.ifas.ufl.edu/index.html and enter pruning in the search box . This link also has a wealth of info on citrus in general as well as your exact tree .
June is the month to fertilize your in-ground tree . Use any good citrus fertilizer and follow the directions on the bag . I use Sunniland's Citrus fertilizer 4-6-8 and have had fabulous results .
Nice to see another Central Florida citrus grower here . How many trees do you have ?

I have several citrus trees.. grapefruit, lemon, lime, key lime, and oranges. I use 8-3-9 for all of them 3-4 times a year depending on their size.
I recently transplanted my grapefruit tree and it didn't seem to take it too well. Several branches were growing towards the ground. I have read elsewhere that these branches should be pruned.. so, I went ahead and did that today.

Thank you all for your replies...also, thank you for the web site GatorMom. I just moved into this home at the beginning of March and the orange tree was just starting to bloom, it's the only citrus tree here. There were still some old oranges from the previous season on it, they were sweet...but because no one lived here for more than a year to care for it, the oranges were extremely dry from lack of water.
At the start of May...the oranges were about the size of a large marble...now they are about the size of a tennis ball. Is it ok to fertilize it now?

You should fertilize citrus trees roughly every 3 months.

damethod - you might want to try a citrus fertilizer or a fertilizer with less nitrogen = a lower number . Citrus does best with a small amount of new leaf growth each flush . You want the nutrients going towards producing delicious fruit rather than a ton of leaves .
Follow the UF fertilizing guide and you can't go wrong = more fertilizer for young trees and less for older trees . 4 light feedings a year are better than three heavy ones . Any feeding is better than none at all !
I pruned a grapefruit tree today that was encroaching on a Navel . I would rather have more navels than the 400 bushels of grapefruit I got from the one pink grapefruit tree ! Geesh !
Pruning is fine of you are pruning for a good reason - like water sprouts , limbs in the way of the mower or limbs in the way of anything else such as power lines . Otherwise , citrus does not need to be pruned .