diff --git a/libavformat/matroskadec.c b/libavformat/matroskadec.c
index b2bdd5efda..c699ce66b8 100644
--- a/libavformat/matroskadec.c
+++ b/libavformat/matroskadec.c
@@ -2613,6 +2613,14 @@ static int matroska_parse_tracks(AVFormatContext *s)
             ret = matroska_parse_flac(s, track, &extradata_offset);
             if (ret < 0)
                 return ret;
+        } else if (codec_id == AV_CODEC_ID_WAVPACK && track->codec_priv.size < 2) {
+            av_log(matroska->ctx, AV_LOG_INFO, "Assuming WavPack version 4.10 "
+                   "in absence of valid CodecPrivate.\n");
+            extradata_size = 2;
+            extradata = av_mallocz(2 + AV_INPUT_BUFFER_PADDING_SIZE);
+            if (!extradata)
+                return AVERROR(ENOMEM);
+            AV_WL16(extradata, 0x410);
         } else if (codec_id == AV_CODEC_ID_PRORES && track->codec_priv.size == 4) {
             fourcc = AV_RL32(track->codec_priv.data);
         } else if (codec_id == AV_CODEC_ID_VP9 && track->codec_priv.size) {
@@ -3165,9 +3173,10 @@ static int matroska_parse_wavpack(MatroskaTrack *track, uint8_t *src,
     uint16_t ver;
     int ret, offset = 0;
 
-    if (srclen < 12 || track->stream->codecpar->extradata_size < 2)
+    if (srclen < 12)
         return AVERROR_INVALIDDATA;
 
+    av_assert1(track->stream->codecpar->extradata_size >= 2);
     ver = AV_RL16(track->stream->codecpar->extradata);
 
     samples = AV_RL32(src);
diff --git a/tests/fate/matroska.mak b/tests/fate/matroska.mak
index b9ed7322fd..93b5bff89a 100644
--- a/tests/fate/matroska.mak
+++ b/tests/fate/matroska.mak
@@ -17,6 +17,11 @@ fate-matroska-remux: REF = 49a60ef91cf7302ab7276f9373f8a429
 FATE_MATROSKA-$(call ALLYES, MATROSKA_DEMUXER VORBIS_PARSER) += fate-matroska-xiph-lacing
 fate-matroska-xiph-lacing: CMD = framecrc -i $(TARGET_SAMPLES)/mkv/xiph_lacing.mka -c:a copy
 
+# This tests that the Matroska demuxer correctly demuxes WavPack
+# without CodecPrivate; it also tests zlib compressed WavPack.
+FATE_MATROSKA-$(call ALLYES, MATROSKA_DEMUXER ZLIB) += fate-matroska-wavpack-missing-codecprivate
+fate-matroska-wavpack-missing-codecprivate: CMD = framecrc -i $(TARGET_SAMPLES)/mkv/wavpack_missing_codecprivate.mka -c copy
+
 # This tests that the matroska demuxer supports decompressing
 # zlib compressed tracks (both the CodecPrivate as well as the actual frames).
 FATE_MATROSKA-$(call ALLYES, MATROSKA_DEMUXER ZLIB) += fate-matroska-zlib-decompression
diff --git a/tests/ref/fate/matroska-wavpack-missing-codecprivate b/tests/ref/fate/matroska-wavpack-missing-codecprivate
new file mode 100644
index 0000000000..4645a86ff6
--- /dev/null
+++ b/tests/ref/fate/matroska-wavpack-missing-codecprivate
@@ -0,0 +1,9 @@
+#extradata 0:        2, 0x00240014
+#tb 0: 11337/500000000
+#media_type 0: audio
+#codec_id 0: wavpack
+#sample_rate 0: 44100
+#channel_layout 0: 3
+#channel_layout_name 0: stereo
+0,          0,          0,    22051,    14778, 0x02819286
+0,      22051,      22051,    22052,    14756, 0x21976243