This paper presents a speech BERT model to extract embedded prosody information in speech segments for improving the prosody of synthesized speech in neural text-to-speech (TTS). As a pre-trained model, it can learn prosody attributes from a large amount of speech data, which can utilize more data than the original training data used by the target TTS. The embedding is extracted from the previous segment of a fixed length in the proposed BERT. The extracted embedding is then used together with the mel-spectrogram to predict the following segment in the TTS decoder. Experimental results obtained by the Transformer TTS show that the proposed BERT can extract fine-grained, segment-level prosody, which is complementary to utterance-level prosody to improve the final prosody of the TTS speech. The objective distortions measured on a single speaker TTS are reduced between the generated speech and original recordings. Subjective listening tests also show that the proposed approach is favorably preferred over the TTS without the BERT prosody embedding module, for both in-domain and out-of-domain applications. For Microsoft professional, single/multiple speakers and the LJ Speaker in the public database, subjective preference is similarly confirmed with the new BERT prosody embedding. TTS demo audio samples are in https://judy44chen.github.io/TTSSpeechBERT/.