Search for Source of Emily's Quote at the Stanford Library:

I first came across Emily's quote on poetry in my copy of John Bartlett's Familiar Quotations, 13th & Centennial Edition, Little Brown & Co., Boston, 1955, p. 649. The source given is "Quoted in Life and Letters of Emily Dickinson (1924) by Martha Gilbert Dickinson Bianchi". I located this book in the Stanford Green Library (811.3D552Db) and the quote may be found on page 276. No date is given, except "To the same" under a letter "To Colonel T.W. Higginson [August, 1870]. In Letters of Emily Dickinson edited by Mabel Loomis Todd (1951) reprinted from an earlier edition (Boston, 1894), the quote is given on page 265. However, the source is from Colonel Higginson's article in The Atlantic after his interview with Emily Dickinson. Finding the exact source of Emily's quote was inconclusive on the web (see below). Here's a faster and more definitive search through the later editions of The Letters of Emily Dickinson at the Stanford Library.

Here are the entries when I looked up Cynthia Mackenzie's
Concordance to the Letters of Emily Dickinson,
University Press of Colorado, 2000 (PS1541.Z49.M33.2000)

The word "physically" is cited 4 times in Emily's Letters:
1870 342a 2.474 If I feel physically as if the (p. 560)
The word "poetry" is cited only 7 times in Emily's Letters
1870 342a 2.474 1 know that is poetry. If I feel (p. 570)
1870 342a 2.474 2 know that is poetry. These are the (p. 570)

The Letters of Emily Dickinson (Edited by Thomas H. Johnson)
Belknap Press of Harvard University Press, Cambridge, MA, 1958
(PS1541,Z5.A3.V2), Volume 2, pp. 472-474

Letter 342: 16 August 1870
To T.W. Higginson

Dear friend
I will be at Home and glad.
I think you said the 15th.
The incredible never surprises us
because it is the incredible.
                  E. Dickinson

This note was delivered evidently by hand at the Amherst House,
in response to one Higginson sent ED on his arrival, asking if
he might call. She had expected him on the previous day, Monday.
The following letter (BPL) Higginson wrote his wife that evening,
dating it: Amherst/Tuesday 10 P.M.:
[Note: A check on Perpetual Calendar for 1870 shows that August 16 fell on a Tuesday,
so Higginson's letter to his wife was on the same day as Emily wrote to him (Letter 342)]

Letter 342a
I shan't sit up tonight to write you all about E.D. dearest but if
you had read Mrs. Stoddard's novels you could understand a house
where each member runs his or her own selves. Yet I only saw her...
I got here at 2 & leave at 9. E.D. dreamed all night of you (not me) &
next day got my letter proposing to come here!! She only knew of you
through a mention in my notice of Charlotte Hawes.

"Women talk: men are silent: that is why I dread women.
"My father only reads on Sunday— he read lonely & rigorous books."
"If I read a book [and] it makes my whole body so cold no fire can ever warm me,
  I know that is poetry. If I feel physically as if the top of my head were taken off,
  I know that is poetry. These are the only way I know it. Is there any other way?”

"Truth is such a rare thing it is delightful to tell it."
"I find ecstasy in living— the mere sense of living is joy enough"
I asked if she never felt want of employment, never going off the place
& never seeing any visitor "I never thought of conceiving that I could
ever have the slightest approach to such a want in all future time"
(and added) "I feel that I have not expressed myself strongly enough."
She makes all the bread for her father only likes hers & says "& people
must have puddings" this very dreamily, as if they were comets
— so she makes them.
[That evening Higginson made this entry in his diary (HCL):]
To Amherst, arrived there at 2[,] Saw Prest Stearns, Mrs. Banfield &
Miss Dickinson (twice) a remarkable experience, quite equalling my
expectation. A pleasant country town, unspeakablly quiet in the summer aftn.

Search for Source of Emily's Quote on the Web:

Emily Dickinson is not listed among the authors quoted
in the 10th edition of Bartlett's Familiar Quotations (1919).
There's a John Dickinson (1732-1808), but no Emily.

Google search: "Emily Dickinson" + "If I read a book" (383 hits).
Google search: "Emily Dickinson" + "If I read a book" +Letter (67 hits).
Google search: "Emily Dickinson" + "If I read a book" +Letter +Higginson (27 hits).