I realise that more capable people have probably done more interesting things with the data, but according to the Perseus vocabulary tool...
In the contemporary works listed below, there are 32,149 individual words in a total word-count of 2,688,531 words, with 6,644 (0.25% of the total word count) occurring once, (but still presumably being understandable by the audience reading that work).
Important as it is to classical scholarship, I'm inclined to (but didn't) leave out
The Deipnosophists of Athenaeus, because its many quotations of classical authours probably skew the data a bit. Not including that work reduces the number of lexical items to 27,559 individual words. In fact, that work alone contributes 2,178 (!!) words occurring once to the total of words occurring once, so without including it, the number of words occurring once comes down to 4,466. (For the sake of comparison, there are 1,119 words (0.8% of the word count) which occur once within the New Testament corpus of texts).
Including
The Deipnosophists of Athenaeus goes against the general idea that the more extensively one reads, the less likely one us to come across a word for the first time.
- Achilles Tatius, Leucippe et Clitophon (ed. Rudolf Hercher)
Aelian, Epistulae Rusticae (ed. Rudolf Hercher)
Aelian, Varia Historia (ed. Rudolf Hercher)
Antiphon, Speeches (ed. K. J. Maidment)
Appian, The Civil Wars (ed. L. Mendelssohn)
Appian, The Foreign Wars (ed. L. Mendelssohn)
Aretaeus, The Extant Works of Aretaeus, The Cappadocian. (ed. Francis Adams LL.D.)
Arrian, Acies Contra Alanos (ed. Rudolf Hercher, Alfred Eberhard)
Arrian, Anabasis (ed. A.G. Roos)
Arrian, Cynegeticus (ed. Rudolf Hercher, Alfred Eberhard)
Arrian, Indica (ed. Rudolf Hercher, Alfred Eberhard)
Arrian, Periplus Ponti Euxini (ed. Rudolf Hercher, Alfred Eberhard)
Arrian, Tactica (ed. Rudolf Hercher, Alfred Eberhard)
Asclepiodotus, Tactica (ed. William Abbott Oldfather)
Athenaeus, The Deipnosophists (ed. Charles Burton Gulick)
Marcus Aurelius, M. Antonius Imperator Ad Se Ipsum (ed. Jan Hendrik Leopold)
Barnabas, Barnabae Epistula (ed. Kirsopp Lake)
Chariton, De Chaerea et Callirhoe (ed. Rudolf Hercher)
Clement of Alexandria, Protrepticus (ed. G.W. Butterworth)
Clement of Alexandria, Exhortation to Endurance, or to the Newly Baptized (ed. G.W. Butterworth)
Clement of Alexandria, Quis Dis Salvetur (ed. G.W. Butterworth)
Cassius Dio Cocceianus, Historiae Romanae (ed. Earnest Cary, Herbert Baldwin Foster)
Dio Chrysostom, Orationes (ed. J. de Arnim)
Diodorus Siculus, Bibliotheca Historica, Books I-V (ed. Immanuel Bekker, Ludwig Dindorf, Friedrich Vogel, Immanel Bekker)
Diodorus Siculus, Bibliotheca Historica, Books XVIII-XX (ed. Immanuel Bekker, Ludwig Dindorf, Friedrich Vogel, Kurt Theodor Fischer, Immanel Bekker)
Diodorus Siculus, Library
Diogenes Laertius, Lives of Eminent Philosophers (ed. R.D. Hicks)
Dionysius of Halicarnassus, De Isaeo (ed. Hermann Usener)
Dionysius of Halicarnassus, De Isocrate (ed. Hermann Usener)
Dionysius of Halicarnassus, Libri secundi de antiquis oratoribus reliquiae (ed. Hermann Usener)
Dionysius of Halicarnassus, Ad Ammaeum (ed. Hermann Usener)
Dionysius of Halicarnassus, De Dinarcho (ed. Hermann Usener)
Dionysius of Halicarnassus, De Thucydide (ed. Hermann Usener)
Dionysius of Halicarnassus, De Thucydidis idiomatibus (epistula ad Ammaeum) (ed. Hermann Usener)
Dionysius of Halicarnassus, De Compositione Verborum (ed. Ludwig Radermacher)
Dionysius of Halicarnassus, Epistula ad Pompeium Geminum (ed. Ludwig Radermacher)
Dionysius of Halicarnassus, De Demosthene (ed. Hermann Usener)
Dionysius of Halicarnassus, Antiquitates Romanae, Books I-XX (ed. Karl Jacoby)
Dionysius of Halicarnassus, De antiquis oratoribus (ed. Hermann Usener)
Dionysius of Halicarnassus, De Lysia (ed. Hermann Usener)
Epictetus, Works
Galen, On the Natural Faculties. (ed. A.J. Brock)
Harpocration, Valerius, Lexicon in decem oratores Atticos (ed. Wilhelm Dindorf)
Flavius Josephus, De bello Judaico libri vii (ed. B. Niese)
Flavius Josephus, Josephi vita (ed. B. Niese)
Longus, Daphnis & Chloe (ed. Rudolf Hercher)
Lucian, Abdicatus (ed. A. M. Harmon)
Lucian, Adversus indoctum et libros multos ementem (ed. A. M. Harmon)
Lucian, Alexander (ed. A. M. Harmon)
Lucian, Anacharsis (ed. A. M. Harmon)
Lucian, Apologia (ed. Karl Jacobitz)
Lucian, Bacchus (ed. A. M. Harmon)
Lucian, Bis accusatus sive tribunalia (ed. A. M. Harmon)
Lucian, Calumniae non temere credundum (ed. A. M. Harmon)
Lucian, Cataplus (ed. A. M. Harmon)