diff --git a/hdbscan/hdbscan_.py b/hdbscan/hdbscan_.py
index 9b8965f0..e29e2af4 100644
--- a/hdbscan/hdbscan_.py
+++ b/hdbscan/hdbscan_.py
@@ -71,6 +71,13 @@ def _hdbscan_generic(X, min_samples=5, alpha=1.0, metric='minkowski', p=2,
         distance_matrix = pairwise_distances(X, metric=metric, p=p)
     elif metric == 'arccos':
         distance_matrix = pairwise_distances(X, metric='cosine', **kwargs)
+    elif metric == 'precomputed':
+        # Treating this case explicitly, instead of letting
+        #   sklearn.metrics.pairwise_distances handle it,
+        #   enables the usage of numpy.inf in the distance
+        #   matrix to indicate missing distance information.
+        # TODO: Check if copying is necessary
+        distance_matrix = X.copy()
     else:
         distance_matrix = pairwise_distances(X, metric=metric, **kwargs)
 
@@ -86,6 +93,13 @@ def _hdbscan_generic(X, min_samples=5, alpha=1.0, metric='minkowski', p=2,
 
     min_spanning_tree = mst_linkage_core(mutual_reachability_)
 
+    # Warn if the MST couldn't be constructed around the missing distances
+    if np.isinf(min_spanning_tree.T[2]).any():
+        warn('The minimum spanning tree contains edge weights with value '
+             'infinity. Potentially, you are missing too many distances '
+             'in the initial distance matrix for the given neighborhood '
+             'size.', UserWarning)
+
     # mst_linkage_core does not generate a full minimal spanning tree
     # If a tree is required then we must build the edges from the information
     # returned by mst_linkage_core (i.e. just the order of points to be merged)
@@ -282,6 +296,14 @@ def _hdbscan_boruvka_balltree(X, min_samples=5, alpha=1.0,
         return single_linkage_tree, None
 
 
+def check_precomputed_distance_matrix(X):
+    """Perform check_array(X) after removing infinite values (numpy.inf) from the given distance matrix.
+    """
+    tmp = X.copy()
+    tmp[np.isinf(tmp)] = 1
+    check_array(tmp)
+
+
 def hdbscan(X, min_cluster_size=5, min_samples=None, alpha=1.0,
             metric='minkowski', p=2, leaf_size=40,
             algorithm='best', memory=Memory(cachedir=None, verbose=0),
@@ -464,7 +486,13 @@ def hdbscan(X, min_cluster_size=5, min_samples=None, alpha=1.0,
                          'Should be one of: "eom", "leaf"\n')
 
     # Checks input and converts to an nd-array where possible
-    X = check_array(X, accept_sparse='csr')
+    if metric != 'precomputed' or issparse(X):
+        X = check_array(X, accept_sparse='csr')
+    else:
+        # Only non-sparse, precomputed distance matrices are handled here
+        #   and thereby allowed to contain numpy.inf for missing distances
+        check_precomputed_distance_matrix(X)
+
     # Python 2 and 3 compliant string_type checking
     if isinstance(memory, six.string_types):
         memory = Memory(cachedir=memory, verbose=0)
@@ -798,9 +826,16 @@ def fit(self, X, y=None):
         self : object
             Returns self
         """
-        X = check_array(X, accept_sparse='csr')
         if self.metric != 'precomputed':
+            X = check_array(X, accept_sparse='csr')
             self._raw_data = X
+        elif issparse(X):
+            # Handle sparse precomputed distance matrices separately
+            X = check_array(X, accept_sparse='csr')
+        else:
+            # Only non-sparse, precomputed distance matrices are allowed
+            #   to have numpy.inf values indicating missing distances
+            check_precomputed_distance_matrix(X)
 
         kwargs = self.get_params()
         # prediction data only applies to the persistent model, so remove