As mentioned by larsmans, LabelEncoder() only takes a 1-d array as an argument. That said, it is quite easy to roll your own label encoder that operates on multiple columns of your choosing, and returns a transformed dataframe. My code here is based in part on Zac Stewart's excellent blog post found here.

Creating a custom encoder involves simply creating a class that responds to the fit(), transform(), and fit_transform() methods. In your case, a good start might be something like this:

import pandas as pd
from sklearn.preprocessing import LabelEncoder
from sklearn.pipeline import Pipeline

# Create some toy data in a Pandas dataframe
fruit_data = pd.DataFrame({
    'fruit':  ['apple','orange','pear','orange'],
    'color':  ['red','orange','green','green'],
    'weight': [5,6,3,4]
})

class MultiColumnLabelEncoder:
    def __init__(self,columns = None):
        self.columns = columns # array of column names to encode

    def fit(self,X,y=None):
        return self # not relevant here

    def transform(self,X):
        '''
        Transforms columns of X specified in self.columns using
        LabelEncoder(). If no columns specified, transforms all
        columns in X.
        '''
        output = X.copy()
        if self.columns is not None:
            for col in self.columns:
                output[col] = LabelEncoder().fit_transform(output[col])
        else:
            for colname,col in output.iteritems():
                output[colname] = LabelEncoder().fit_transform(col)
        return output

    def fit_transform(self,X,y=None):
        return self.fit(X,y).transform(X)

Suppose we want to encode our two categorical attributes (fruit and color), while leaving the numeric attribute weight alone. We could do this as follows:

MultiColumnLabelEncoder(columns = ['fruit','color']).fit_transform(fruit_data)

Which transforms our fruit_data dataset from

to

Passing it a dataframe consisting entirely of categorical variables and omitting the columns parameter will result in every column being encoded (which I believe is what you were originally looking for):

MultiColumnLabelEncoder().fit_transform(fruit_data.drop('weight',axis=1))

This transforms

to

.

Note that it'll probably choke when it tries to encode attributes that are already numeric (add some code to handle this if you like).

Another nice feature about this is that we can use this custom transformer in a pipeline:

encoding_pipeline = Pipeline([
    ('encoding',MultiColumnLabelEncoder(columns=['fruit','color']))
    # add more pipeline steps as needed
])
encoding_pipeline.fit_transform(fruit_data)

While AN6U5 has given a very good answer, I wanted to add a few points for future reference. When considering One Hot Encoding(OHE) and Label Encoding, we must try and understand what model you are trying to build. Namely the two categories of model we will be considering are:

1. Tree Based Models: Gradient Boosted Decision Trees and Random Forests.
2. Non-Tree Based Models: Linear, kNN or Neural Network based.

Let's consider when to apply OHE and when to apply Label Encoding while building tree based models.

We apply OHE when:

1. When the values that are close to each other in the label encoding correspond to target values that aren't close (non-linear data).
2. When the categorical feature is not ordinal (dog, cat, mouse).

We apply Label encoding when:

1. The categorical feature is ordinal (Jr. kg, Sr. kg, Primary school, high school, etc).
2. When we can come up with a label encoder that assigns close labels to similar categories: This leads to less splits in the trees hence reducing the execution time.
3. When the number of categorical features in the dataset is huge: One-hot encoding a categorical feature with huge number of values can lead to (1) high memory consumption and (2) the case when non-categorical features are rarely used by model. You can deal with the 1st case if you employ sparse matrices. The 2nd case can occur if you build a tree using only a subset of features. For example, if you have 9 numeric features and 1 categorical with 100 unique values and you one-hot-encoded that categorical feature, you will get 109 features. If a tree is built with only a subset of features, initial 9 numeric features will rarely be used. In this case, you can increase the parameter controlling size of this subset. In xgboost it is called colsample_bytree, in sklearn's Random Forest max_features.

In case you want to continue with OHE, as @AN6U5 suggested, you might want to combine PCA with OHE.

Let's consider when to apply OHE and Label Encoding while building non tree based models.

To apply Label encoding, the dependance between feature and target must be linear in order for Label Encoding to be utilised effectively.

Similarly, in case the dependance is non-linear, you might want to use OHE for the same.

Note: Some of the explanation has been referenced from How to Win a Data Science Competition from Coursera.