The Gemara (Menahot 40b) says that the minimum size of a garment which would require Tzitziot for a Talit Katan is the size of a garment that a child would wear to go out alone to the marketplace. The Ben Ish Hai (Rav Pe’alim vol. II, § 6) takes a lenient approach that a blessing can be recited on a Talit Katan that is 1 Amah by 1.5 Amot and. According to Rabbi Haim Palagi, the minimum length of each side would be 1.5 Amot, which is approximately 72 cm or 28 inches, Rabbi Ben Zion Abba Shaul (Or Lezion vol. II, ch. 2) says that one should not recite a blessing on a garment that is smaller than this.
Rabbi Ovadia Yosef (Yabia Omer, vol. IX, Orah Haim, § 100) takes a different approach and cites opinions that one only recites a blessing on a Talit Katanthat is long enough to reach one’s knees and that the minimum length is calculated using an adult as a model and not a child. As such, he invokes the concept of Safek Berachot Lehakel and says one should not recite a blessing on a Talit Katan.
The Poskim of the Maghreb appear to be less bothered by the possibility of reciting a blessing in vain. For example, Rabbi David Cohen-Scali of Oran, Algeria (Kiryat Hana David, vol. I, § 4) cites the Zohar (Pinhas), and says that the minimum length per side is 1.25 Amot, which is roughly 24 inches or 50 cm and one would be able to recite a blessing on such a Talit Katan. He also quotes the Siddur Bet Oved who in turn cites Rabbi Shneur Zalman of Liadi, who says that the minimum size of garment that could be used for a Talit Katanis 1 Amah by 1 Amah, or 48 cm/19in. per side. A good guideline to follow is that a blessing should recited so long as the Talit Katan is at least 24 inches by 24 inches, as rules Rabbi Haim Palagi. However, there is a Halachic basis on which to rely if one recites a blessing on a Talit Katan that is even only 1 Amahby 1 Amah. It should be noted that one only recites a blessing on a Talit Katanin certain situations, and one may refer to that Halacha for details.
Summary: One should recite a blessing on a Talit Katan that is at least 24 inches by 24 inches.