Your doubt is reasonable here as the grammar is very basic concept in English.
You want to know that "The Ganga is a sacred river" is this sentence is right or not?
The above mentioned sentence is correct due to use of article i.e. "The".
If you would use A in place of The, that sentence would be wrong grammatically. Because use of "The" is compulsory when we addressed any river, ocean etc.
And here in your sentence Ganga is a holy river. So use of "The" is compulsory.