You may be able to find vegetarian Grana Padano style cheese, but I don't think you will find the real thing in vegetarian form.
This is because the making of Grana Padano is still a traditional process and true GP cheese is only produced in certain regions of Italy.
It in fact has P.D.O. (Protected Designation of Origin) status, which means that only those cheeses produced in certain regions and using certain methods can legally be called Grana Padano.
I imagine one of those methods is using animal rennet.
I would be surprised that there isn't some form of substitute available in Italy, as they have the highest proportion of vegetarians in Europe at 10%.
I get the feeling, however, that they are perhaps less zealous about it than others if it means giving up good cheese.
The only suggestion I have found as an alternative to GP as something to sprinkle on pasta etc is nutritional yeast powder, which apparently has a similar nutty, creamy taste.
Not ideal, but if you make the choice to be veggie you have to take the rough with the smooth!
I see from your profile that you live in the UK; we are lucky in that we have a lot of fantastic small local producers, so it may be worth looking up some local dairies or cheesemakers and seeing if they can offer an alternative.
cooking.stackexchange.com/users/4194/ElendilTheTall
I Buy kosher Grana Padano: http://www.collaspa.it/en/index.php Since we can't use animal rennet
,it is vegetarian and it says so on their web page.
cooking.stackexchange.com/users/25091/Rachel
You can get a cheese named Grandi Pascoli from QuatrtroColli.
Its is a grana padano made With vegetable rennet.
This is especially made for vegetarian use.
cooking.stackexchange.com/users/50403/Andreas
No. Grana Padano's traditional recipe uses animal rennett and because it has DOP protection under EU law, no cheese made to any other recipe can be sold as 'Grana Padano'.
cooking.stackexchange.com/users/14817/Vince Bowdren
Try Grana Padano Tipo, which contains a modified enzyme.
It's used by a leading vegetarian restaurant in Brighton, for its full flavour.
cooking.stackexchange.com/users/18898/DANIEL JETER
I believe the best vegetarian alternative is Gran Mantovano .
It's made in Italy by a reputable maker of Grana Padano and Parmigiano Reggiano and
in my opinion is an excellent substitute for Grana Padano.
It is made specifically for vegetarians.
cooking.stackexchange.com/users/83726/kpg
There is indeed a fabulous Italian Hard Cheese that is Vegetarian.
It's called Quattrocento and is made by Granarolo.
You can buy it at Waitrose or from idelionline.com
It's a smoother texture but still packs a punch so cooks and eats the same as a parmesan or PDO product
It is made with microbial rennet and is preservative free so a much cleaner ingredient deck than a few other cheeses of a similar style
cooking.stackexchange.com/users/70792/E11i3 M
My wife is vegetarian and, since meeting her, I've come to realise that all Grana Padano seems to be non-vegetarian. Is this really the case, or are my local supermarkets just not stocking the veggie stuff? Would be a shame for her to miss out on so many things (esp. pesto) just because of this.  Thanks.
Is it possible to get vegetarian grana padano cheese?
cooking.stackexchange.com
<cheese><vegetarian>
cooking.stackexchange.com/questions/18227
cooking.stackexchange.com/users/562/Mal Ross
Vegetarian Grana Padano-style cheeses include Kosher Grana Padano, which does not use animal rennet, Grandi Pascoli from QuatrtroColli, Gran Mantovano and Quattrocento from Granarolo. You can't buy Grana padano without animal rennet. You can also try Grandi Pascoli, Gran Mantovano or Quattrocento.
Grana Padano can't be made without animal rennet. Try buying a kosher version. You can replace with Grandi Pascoli, Gran Mantovano or Quattrocento.