MS supervisor offered a low-paying PhD position; can I ask for a reference to work in a different lab instead?
If you are looking for other PhD positions within Germany you may not need to ask for a reference: reference letters are not as common here as in some other countries. However, if you had an employment contract before, ask for your "Arbeitszeugnis" which pretty much takes the role of a reference letter. You are by law entitled to that, so asking for that should be a pretty standard request and you can say you'd like to have it for the sake of having your paperwork complete.
In case you were there just as Master student you don't get an Arbeitszeugnis, the certificates for final exam and Master thesis take that role. 
I'm entirely with @cag51 in that your primary decision should be about the field/topics.
This is a perfectly fine reason to leave the group you are now in, and the professor should understand that. 
Assuming the financial side is the only consideration that drives you away from the scholarship, I'd recommend being open with the professor about this. I'd assume an engineering professor to be able to calculate and the immediate difference in money is rather obvious (see below).  The professor may have further arguments in favor of the scholarship (see below), and there may be some space for negotiations.
If on the other hand, it turns out to be financially infeasible to do the PhD with the scholarship, the professor should again be willing to support you in looking for a job in the form of a reference.
(This assumes that the professor is neutral or benevolent towards you - wich is consistent with the offered scholarship)
OTOH, if you "secretly" apply for other positions but are not accepted and end up with the scholarship and the professor then finds out, this may create bad blood (not trustworthy, not open, etc.) - and a PhD is a rather intense and lengthy period of work where the professor may very well have thoughts into which students to "invest", say, money to attend conferences and which students are likely to run away as soon as there's the possibility. So I'd consider this approach somewhat risky here. 
In other words, while it may be doable to apply for the other positions without a reference, I'd recommend to ask the professor for a reference letter.  




Some thoughts about scholarship vs. PhD position via employment contract. It is not that easy to judge what amount of scholarship would be equivalent to what wage (though your offer seems to me to be rather on the low side):


1100 €/month scholarship will financially be comparable with an "employee" gross wage of 915 € or a net wage of 725 €/month. As you'll have to take care of your social insurance by your own (I'm assuming that even if you don't have to pay e.g. into pension scheme it would be sensible to put away at least as much as an employee in a similar financial situation is forced to put aside). If you decide against any social insurance that is not mandatory, i.e. only pay health and long term care insurance, you'll have ≈ 940 €/month.
As you say, it should be comparatively easy to find jobs that pay more: a 50 % TVL E13 in level I (first year) will be ≈1275 € net/month, so there should be other "features" of the scholarship to get it at par.
But scholarships often do come with additional features such as some money that you can spend at your discretion for your research (say, 200 € Büchergeld = money for books [which I could keep afterwards], I had a scholarship with additional money for travel to conferences and research stays and to purchase small things for the lab [they stayed with the university when I left]). You cannot take those things 1:1 like a higher scholarship, as e.g. university/your project rather than you personally should pay for conferences - but those sources are often very limited, so e.g. I did attend far more conferences than my fellow PhD students in the same group (typical was one national vs. several international + research stay for me).
Find out about this. 
Scholarships may or may not allow you to work a side job. Check this carefully. If you can, you may be better off with getting a well-paying side job for a few hours per week.  
In any case, check carefully how much you are supposed to work on other projects but your PhD project. This is unusual now, but my initial employment contracts as PhD student did not pay for any of my PhD thesis research work but were entirely about teaching lab/practica.
If you are anyways expected to be contributing to the institute's teaching load, you may be able to ask for an employment contract for that in addition to your scholarship, whereas a PhD student employment contract may include already a duty to help so many hours with teaching. 
Scholarships are not employment contracts. Some of the consequences are: You are not subject to Arbeitnehmererfindungsgesetz (employee invention law) nor to the employee paragraphs of copyright law: in consequence inventions and e.g. software you develop is completely owned by you, not by the university.
Also, the scholarship is not subject to income tax. OTOH, your PhD years will not count towards years contributed towards the governmental pension scheme unless you sign up for voluntary contributions (AFAIK, that is possible).
Scholarships often offer possibilities such as attending workshops and courses on particular subjects, and to network with people from other universities and other fields.  
Depending a bit on the scholarship, it may be a good boost to your CV. Scholarships are not that common in Germany, so having had one means that you were selected, e.g. for being a very good student.
(side note: because of this, I find it unusual that the professor offers you a scholarship as opposed to offering that they'd help/try to get you a scholarship. Still, it is entirely possible.)