It's up to you to convince the consulate that you do fulfill all the requirements and if bank statements are missing they are going to suspect you are trying to hide something, which does not help your application.
As far as the “means of subsistence” requirement is concerned, you need a specific amount of cash per day plus enough money to pay for the flight. But if your uncle is ready to cover the accommodation costs and the flight tickets, you would theoretically not need to have much money on your bank account.
For your uncle support to count in a Schengen visa application, you would usually need more than a letter, namely some sort of “certificate” issued by the police or the town where your host lives and some proof of his income/financial means (e.g. his bank statements). I do not read Czech and have no experience with visas for this particular country, but some info I found does suggest it's the same in the Czech Republic (see e.g. policie.cz and mzv.cz).
The problem is that bank statements can also go a long way towards fulfilling another requirement, namely providing assurances that you will return to your country of residence at the end of the visa. Here the point is not whether you have a lot of money on the account right now but whether you get a regular income. That's why consulates usually require three months worth of bank statements and not merely your last statement.
If you have some other way to establish your ties to your country of origin (a spouse staying behind, a house you own, maybe even simply a university registration) and you submit a proper certificate + proof of funds from your uncle, you might be able to get a visa without providing your own bank statements but it would in any case weaken your application. And if you have no way to show tangible ties to your place of residence (e.g. you are young with no family of your own, have a cash-only job and no property), getting a visa could be incredibly difficult, even with an invitation.