Learn English – Comma or period after “No”

Like others suggested, a dash (not a hyphen, be careful) or a colon are the most appropriated choices, but I'd exclude the comma. The examples would be as follows:

• I am curious — what is the time?
• I am curious: what is the time?

The comma must be excluded because it would constitute a comma splice, since it must be used along with a coordinator (and, but, not, so, etc). A semicolon can be adopted but sometimes it requires a conjunctive adverb at the beginning of the second clause (see hence, for example), so it depends on the case.

You don't have to end the sentence with a period; in this case you wouldn't. A period separates completely two ideas and in your example they are related so a period would not be advisable.

What's sure is that you can't avoid to use something. If you don't put anything between the two clauses, you'll end up writing a run-on sentence. In order to make it clearer about it, look at the example below, which shows a run-on sentence. It doesn't make much sense:

I am curious what is the time?

You can understand its meaning of course, but considering syntax rules, it's grammatically incorrect.

As Robusto points out in comments beneath the question, there is no universally acknowledged rule governing whether to include or omit a comma after a conjunction at the beginning of a sentence. Robusto reports preferring to include such commas in academic documents, but many other writers and editors would not include them.

In my experience copyediting manuscripts for book publishers (including university presses) and later for magazine publishers, I don't recall ever having encountered a house style that required adding a comma after "And," "But," or the like. To the contrary, most house styles either said nothing at all on the subject or recommended omitting such commas, presumably for the reason that Words Into Type, third edition (1984) gives at the start of its long section on comma usage:

A comma should be used only if it makes the meaning clearer or enables the reader to grasp the relation of parts more quickly. Intruded commas are worse than omitted ones, but keep in mind at all times that the primary purpose of the comma is to prevent misreading.

The argument for including a comma after an opening conjunction is not, I think, grounded in a desire to make the meaning clearer (since the meaning tends to be quite clear without the comma, as Peter Shor indicates in a comment above), but rather in a desire to demarcate with exactitude the boundaries of the parenthetical expression that follows. Why Gregg Reference Manual would insist on such precision at the beginning of a sentence but not in the middle of one is a mystery to me.

There is nothing inherently wrong with using commas to break out parenthetical phrases regardless of where they appear in a sentence: It increases the number of commas in a work while (arguably) not making the sense of the text any clearer; but it's a style decision, and style decisions—if followed consistently—don't need to be justified.

On the other hand, if you don't want to add a comma after a conjunction at the start of a sentence, I don't think that you should consider yourself to be under any obligation to the preferences of Gregg Reference Manual unless your publisher has instructed you to obey it.