"Does an introductory clause or phrase need a comma after it?"
It is appropriate to use a comma after an introductory a) clause, b) phrase, or c) word that comes before the main clause:
a) Because it was snowing, the flight was delayed.
b) Having completed her work, she went to bed.
c) Yes, you should eat a healthy breakfast.
Use a comma to set off an introductory clause beginning with these frequently used words: after, although, as, because, if, since, when, while.
A comma should be used after an introductory prepositional phrase to avoid misreading: In all, four students failed the class.
In addition, single introductory words should also be followed by a comma: however, well, yes, unfortunately, etc.
W.W. Norton lists a stylistic exception: "To accelerate the pace of their sentences, writers sometimes skip the comma after an introductory adverb or short introductory phrase" (p. 455).